  We establish the well-posedness of SDE with the additive noise when a
singular drift belongs to the critical spaces. We prove that if the drift
belongs to the Orlicz-critical space $L^{q,1}([0,T],L^p_x)$ for $p,q\in
(1,\infty)$ satisfying $\frac{2}{q}+\frac{d}{p} =1$, then the corresponding SDE
admits a unique strong solution. We also derive the Sobolev regularity of a
solution under the Orlicz-critical condition.
