An electro-mechanical transmission is provided having only a single motor/generator, at least one differential gear set and two torque-transmitting mechanisms. A first of the torque-transmitting mechanisms is selectively engageable to establish a first continuously variable operating mode and a second of the torque-transmitting mechanisms selectively engageable to establish a second continuously variable operating mode and a synchronous shift between the two operating modes is achievable. A method of control is provided in which vehicle operating characteristics are analyzed to identify a target operating state in terms of operating mode and ratio based on the available motor torque and motor power and on maximizing energy efficiency. The transmission is controlled to approach this operating mode as closely as possible and the diverge away from the optimum torque operating with zero net battery use as the battery charge of the battery connected with the motor/generator accumulates or depletes.