In 1920 he was a member of the Swedish ice hockey team which finished fourth in the 1920 Olympics. He played five matches and scored four goals. Eric Burman became the first goal scorer for Sweden ever, by scoring against Belgium, April 23, 1920.
Four years later he finished again fourth with the Swedish team in the 1924 Olympics.
He later returned to Sweden, and in November 26, 1940 Eric Burman became the oldest player ever in Swedish championships in hockey. In this match he also became the oldest ever scorer in Swedish in the same game. He was then 42 years, 11 months and 20 days, when IK Göta played IK Sture in Svenska Serien, the highest league in Swedish ice hockey between seasons 1935/1936 through 1943/1944.