Determine angle of reflection without magnitudes

I realize this question has been answered before, but not yet in terms I understand.

In code I'm bouncing two balls off each other. I know each ball's current direction in radians, and I can find the normal angle using the atan2() function.

Say I ignore one ball and focus on the other - I have an angle of incidence, and a normal angle. Is there a straightforward way to find the angle of reflection without needing magnitudes?