Is there any theorem which states any general linear connection can be decomposed into another linear connection plus the contortion tensor ? i didn't find any References
Check out Kobayashi and Nomizu's Foundations of Differential Geometry, Volume 1. On page 159, when proving the existence of the Levi-Civita connection (Theorem IV.2.2), they pick an arbitrary metric connection and add the contorsion tensor to it and show that it is a metric connection with vanishing torsion. Hence any metric connection can be written as the difference of the Levi-Civita connection and its contorsion tensor.
Another reference is Section 7.2.6 of Nakahara's Geometry, Topology, and Physics. See equations (7.30)-(7.35) for Nakahara's derivation.