Thread: Tell me how to solve this

I've spent hours trying to figure this out. I'm building a particle engine for my thesis and I am having a hard time with this part of it.

I have two particles colliding and I need to know their resulting trajectories.

I know:

Mass of both particles
Velocities of both particles (both angle, magnitude and in vectors)
I know the angle between them

Attached is a diagram.

The distance between the two and the radii of them need to be irrelevant.