The four branch differential Transmission System, ("FBD"), comprises a first input shaft and a second output shaft. Furthermore there are third and fourth shafts which are respectively connected to first and second variators which control the speed (or torque) of the shaft, to which they are connected. Each variator can, for instance, be an electric motor which can adjust the speed of these shafts. The four shafts (branches) of the FBD are connected directly or indirectly via gears. The FBD comprises spur gear planetary gearsets. There is no requirement for a ring gear. The FBD includes two planetary gearsets using several spur gear suns and planets, which form a combination of a plus planetary gearset and a minus planetary gearset.