A transmission for a vehicle, particularly a skid-steered vehicle, that employs motive power from a prime mover delivered through an input shaft to drive left and right drive shafts at a nominal speed and input power from an electric motor to vary the speed of the left and right drive shafts according to steering commands from a steering control structure. The speed of the left and right drive shafts is directly related to a speed of the input shaft and the nominal speed of the left or right drive shaft is varied upwardly or downwardly by a ratio of the speed of the steering shaft via a speed varying structure. The speed of the left and right drive shafts is simultaneously varied in opposite directions (i.e. upwardly and downwardly) relative to the nominal speed by an equal number of rotations.