DC motor back emf and supply voltage
Supply voltage = Eb + armature current x armature resistance. The solution apparently assumes that the armature resistance is negligible. In other words, the motor is assumed to have 100% efficiency. Note that torque delivered to the load is torque developed minus internal motor friction torque and aerodynamic drag torque acting on the rotor. Also no mention is made of any power required for the motor field, so the motor either has permanent magnets or the field power is also neglected.