Promising Swedish driver in the lower formula, he failed to realise his full potential as he moved up to F2 and F3000. Had a test with McLaren in 1979 but a GP drive never materialised.
In 1977 Eje raced a Chevron B38 Toyota, competing in the British BP Formula 3 Championship finishing 2nd on 56 points, taking three wins on the way and the Vandervell Formula 3 Championship where he finished 5th.
Suitably encouraged, fellow Swede Torsten Palm took Eje under his wing. He moved up to European Formula 2 in 1978 with Fred Opert Racing driving a Chevron B42 Hart, but it was a dissapointing year finishing 11th in the series with just one podium to show for his efforts.
However he picked up a testing contract with McLaren in 1979 while continuing in European F2 with Marlboro Team Tiga. He finished 9th in the Championship with one win and two podium finishes.
In 1980 he raced a Maurer MM80 a few times without any luck but in 1981 he was back on form driving for Maurer Motorsport with the MM81 and ending the season in third place in the F2 Championship and winning the Gran Premio di Roma. However the run did not continue and he only did 2 F2 races in 1982.
He headed for Japan in 1983 to compete in their F2 series and also competed in the Macau F3 GP driving a Hayashi 322 Toyota to a respectable 4th place on aggregate.
He continued to race in Japan in 1984, 1985 and 1986 without doing anything of any note, though he did have two podium finishes in '85 and one in '86.
In 1987 Japanese F2 switched to F3000 but Eje performances remained constant thoughout the '87 season and the next.
A switch to sports cars followed in 1989 where he continued to race a Porsche 962C for various teams until the early 1990s