Joseph Jordan lived in Gorton, Manchester, and in Reddish, Stockport. He owned a boot and shoe repair shop in Oldham, Lancashire, with his brother John until 1963.

In 1934, he developed a non-flammable celluloid shoe heel with his brother, which could be illuminated by an internal lightbulb. The brothers worked on a variety of styles, shapes and colours which were intended to match the outfits worn by dancers in chorus lines. It was the brothers' intention to create jobs for local unemployed workers through the manufacture of the heels.

Joseph Jordan went on to develop other ideas, such as electrical equipment to ensure safe landing of aircraft in darkness, fog and mist, and anti-dazzle glasses for car drivers. None of his inventions went into production.