He became a student of Oscar Matthiesen in Copenhagen in 1896. Erdmann followed Matthiesen to Berlin and Munich and also visited France and Italy. This was where he learned fresco techniques, decorative painting, and church restoration.
After he returned to Norway in 1903, he worked together with Eilif Peterssen on decorating Ullern Church in Oslo.
Erdmann studied church restoration in Denmark in 1912, and was made a conservation adviser in 1919.