Edward worked for his father when he was young. However, after the middle brother who was apprenticed to John died, Edward went to London in 1773 to become an apprentice mathematical instrument maker with his brother John Troughton. McConnell writes :-
At this time John Troughton worked for other craftsmen, who brought their sextants and small astronomical quadrants to be divided in his workshop, for he enjoyed a high reputation in this difficult art, which was performed entirely by hand. Between 1775 and 1778 John constructed a dividing engine, on the lines of that recently designed by Jesse Ramsden, by which he was able to increase both his accuracy and his rate of work.Edward Troughton took the science of instrument-making very seriously indeed and began to study the mathematical background necessary, as well as astronomy so that he could understand precisely how the instruments were being used and the type of scientific discoveries that users of the instruments were hoping to make. Edward began to design and to build his own instruments. The business flourished and John was able to expand buying property outside London, as well as the established business of Benjamin Cole at the Sign of the Orrery. This business had a shop at 136 Fleet Street and behind the shop were workrooms where instruments could be constructed. Edward became a partner with his brother and they traded as John and Edward Troughton at The Sign of the Orrery. Soon after this, however, in 1788 John died and Edward Troughton ran the business on his own. He had been able to take on apprentices of his own from 1784 and soon attracted the most promising young men to work for him.
Troughton soon established himself as the leading maker of instruments in England for not only had his brother John died in 1788 but also the other brilliant maker of scientific instruments Ramsden died in 1800. Not only did he make great improvements in the design of existing instruments, but he also invented many new instruments. He began his instrument making career with instruments to aid navigation, for example, he designed the 'pillar' sextant, patented in 1788, the dip sector, the marine barometer and the reflecting circle built in 1796. Other instruments which he designed were for use in surveying. He designed the pyrometer, the mountain barometer and the large theodolites which were used in the American Coast Survey of 1815, and base-line measuring apparatus. In fact these instruments were later used in surveys of Ireland and of India.
Troughton's most famous instruments were astronomical ones. He made the Groombridge Transit Circle in 1805 and a six foot Mural Transit Circle in 1810 which was erected at the Observatory in Greenwich in 1812. In 1816 he made a ten-foot Transit Circle. He never produced any telescopes, however, and the reason for this was that he suffered from colour-blindness which was a defect which ran in his family. He did, however, make use of some of his own instruments to make astronomical observations. For example he observed the transit of Mercury across the disk of the sun in May 1799 and made careful, accurate observations which he published in the scientific literature.
One of Troughton's most important contributions was a method of dividing a circle. His paper on this, An account of the method of dividing astronomical and other instruments by ocular inspection in the Philosophical Transactions of the Royal Society in 1809 won him the Copley medal of the Royal Society. In  this invention is described in detail and also put into context. Brooks writes:-
The development of the circular dividing engine in England is traced from Henry Hindley and Jesse Ramsden through the improvements introduced by Ramsden's successors to the self-acting engine of William Simms. Particular emphasis is given to the invention, evolution and transmission of the methods used to achieve accuracy in dividing the wheel, ratcheting the teeth and matching them to the endless screw, and mounting the cutter. The procedures adopted by Ramsden and Troughton for correcting initial dividing marks are also described.Troughton was elected a fellow of the Royal Society in 1810 largely due to the fact that he had been prepared to share his methods of dividing instruments which he had kept a closely guarded secret up to that time. That he was prepared to write up his methods for publication followed discussions which he had on the topic with Nevil Maskelyne, the astronomer royal. He was also elected a Fellow of the Royal Society of Edinburgh in 1822. In 1822 he published another work A comparison of the repeating circle of Borda with the altitude and azimuth circle in the Memoirs of the Royal Astronomical Society.
After his brother John died, Edward ran the business alone until, in 1826, because of failing health due to old age, he took on a new partner William Simms. Troughton described Simms as the best craftsman h knew, and Simms and his wife came to live with Troughton at his house in Fleet Street. Troughton was by this time over 70 years old and was suffering from some of the ailments of old age such as rheumatism and lumbago. The firm continued to flourish, however, and they supplied George Everest with a number of instruments to conduct his survey of India. (Mount Everest was renamed in George Everest's honour in 1865). Everest had spent 25 years between 1818 and 1843 making a trigonometric survey of India, including measuring the 11.5 degree arc of the meridian from the Himalayas to Cape Comorin, the most southerly point of the Indian subcontinent.
Certainly being an instrument maker was not an easy task and one had to deal with customers with extremely high expectations. For example a dispute which Troughton became involved in towards the end of his life was with Sir James South who was President of the Royal Astronomical Society from 1829 to 1831. This dispute are described in detail in .
You can see an account of the dispute at THIS LINK where we quote from .
It was a sad affair in which South, who had previously been friendly with Troughton, ended up trying to damage his reputation. In fact a court case was still in progress when Troughton died. Simms continued Troughton's internationally known business after Troughton died in 1835 at his home in Fleet Street.
As to Troughton's character and interests some information is given in :-
Troughton never married. His friends described him as a modest man, frugal in habit and somewhat careless in dress, who found relaxation in walking and fishing. Reading was the great pleasure of his later years; his library, auctioned by Sothebys after his death, testified to a broad sweep of interests beyond those related to his craft.
Article by: J J O'Connor and E F Robertson