Exact solution of single contact force with friction?

[Story]

I am working on a simple 2d physics engine for my game. However, I've run into a problem with rotation and friction.

Is there any way to exactly solve (ignoring rounding errors) a single contact point with rotation and friction? For simplicity I'm assuming that one of the bodies is static and there's no restitution. The problem is that friction force has a two sided clamp that varies based on normal force. Also, due to rotation, the two directions are dependent because a normal impulse will also cause tangential acceleration and vice versa. It's not an LCP, and not an MLCP from what I can tell either.
So is there any non iterative algorithm to solve this?

I'm trying to understand block solving and it is frustrating that I can't even figure out the simplest case.