Just two conductors, and they're color coded? That's pretty easy.
Cut off the damaged part, and strip back the outer jacket and the individual wire insulation on both conductors. "Pigtail" the matching conductors, twisting them together as tightly as you can. Insulate the individual splices, and the overall joint, with any kind of tape.
If you had soldering skills, this would be a permanent repair. "Twist & tape" will do for a while, though.