His father was killed during the Warsaw Uprising, and Kulesza himself, who was 13, was lucky to survive, as a German soldier threw him under a passing tank.

After the uprising, he was forcibly taken to Germany as Ost-Arbeiter, but escaped and returned to Poland on foot.

In 1972–1974, Kulesza coached Lechia Gdańsk, and since 1974, he worked with several national teams of Poland, such as U-21 (1974–1975), and U-23 (1975–1978).

In the 1980s, Kulesza worked in Tunisia and Morocco, returning to Poland in late 1980s.

He actively fought corruption, and in 1993, he supported stripping Legia Warsaw of its championship title, after Warsaw's team routed Wisła Kraków 6–0 in Kraków on the Sunday of Miracles.