He received his filosofie kandidat degree from the University College of Gothenburg in 1903, his theology degree from Lund University in 1907, became licentiate there in 1912 and completed his doctorate of theology in 1918.

He was docent of New Testament exegesis in Lund 1913-1924, and was assistant at Uppsala University 1918-1919.

During the 1930s, Eidem expressed nationalist views, but kept a clear distance from the German Nazi regime and warned the Lutheran church in Germany for the prevalent antisemitism.

After the war years, Eidem was one of the churchmen who donated money to the high church St. Ansgar Foundation in Uppsala.

Following the murder of Kaj Munk on 4 January 1944 the Danish resistance newspaper De frie Danske brought condemning reactions from influential Scandinavians, including Eidem.