Goodall was the son of Edward Goodall, the engraver of J.M.W. Turners works, and his brothers were the artists Frederick Goodall (1822–1904), a Royal Academician, and Walter Goodall (1830–89). His sister Eliza Goodall (1827–1916) was also an artist.
Edward Angelo was apprenticed to his fathers office and his own artistic talents came to the fore in his teens when he won a silver medal, and praise from Clarkson Stanfield RA, at the Society of Arts for a picture of the landing of the Lord Mayor at Blackfriars Bridge. His work was exhibited at the Royal Watercolour Society.