Relationship between torque and back-EMF voltage | BLDC motor modeling
If the \$e_a\$, \$i_a\$, etc., are the idealized voltages and currents on the armature, with magnetic and electrical losses neglected, then that equation simply follows from conservation of energy.
Let \$P_e\$ denote electrical power, and \$P_s\$ denote shaft power.  Claim that there's no friction, resistance, or other losses.  Then, in a universe that's not visibly changing dimensions, \$P_e + P_s = 0\$ by conservation of energy.
$$P_e = \sum_{\mathrm{all\ windings}}e_{winding}i_{winding}$$
$$P_s = T_e \omega_m$$
Do an itty bitty bit of math, to substitute \$e_a\$, \$i_a\$, etc., for my pretentious summation over all hypothetical windings, then an itty bitty bit more by dividing both sides by \$\omega_m\$, and you end up with your expression.