A differential gear includes two coaxial gears which are connected by one or more similar planet gears mounted on intermediate shafts.   Those shafts are fixed to a carrier.  The arrangement is such that the angular velocity of the planet gears is the average of the angular velocities of the two co-axial gears.

Differential gears are used universally in automobile drives to allow for differences in driven wheel speeds when cornering

A linear version of the differential gear is shown below.    It is clear from this diagram that the velocity of C = the average of the velocities of A & B.

V_c = V_A + V_B / 2

Considering the type of differential as used for car drives.   In the figure below the drive shaft is connected to the gear A.   This drives the case D via a bevel drive.   The case rotates and drives the wheel drives B and C via the gear E.   If the gear E is fixed then the wheels would rotate at the same speed as the case.   As the the gear E is free to rotate the average speed of the wheels is the same as the case.  Therefore if one wheel locks the second wheel would rotate at twice the speed of the case.

Generally each gear mesh will have 1% - 2% loss in efficiency, so with two different meshes from the transmission shaft to each of the half shafts, the system will actually be 96% to 98% efficient.   If the system is assumed to be 100% efficient; then

Drive Power A = Driven Power B + Driven Power C

P_A = P_B + P_C = T _B ω_B + T _C ω_C

P_x is the power :
T_x is the Torque:
ω_x = the angular velocity.