Edward Felix Goldsmith was born in Foots Cray, Kent, England on 2 June 1903. He qualified as an architect in the mid-1920s and subsequently practised in London. In the early 1930s, with his brother, Humphrey Hugh Goldsmith (1904-1979), he formed a partnership with Francis John Potter (1871-1948) as Frank Potter and F. & H. Goldsmith at 1 Verulam Buildings, Gray's Inn, London. Humphrey Hugh Goldsmith withdrew from the partnership in 1938, however, Edward Felix Goldsmith continued to work with Potter for at least another year.
Edward Felix Goldsmith was elected an Associate of the Royal Institute of British Architects (ARIBA) in 1926. His address was given as 104 Gower Street, London and 1 Verulam Buildings, Gray's Inn, London in 1939. He died in London in 1976.