Speeds high
The critical engine on a jet is the upwind engine, and if four engines (wing mounted) the outboard one.
Imagine taking off on RWY18 with a 30kt easterly blowing. With the tail fin and fuselage aft of the wing/landing gear generally being a larger area than the fuselage forward of the wing/landing gear the tendancy is for the aircraft to weathercock into wind (left in this example). Much as would happen in flight should the nose yaw one way or t'other.
If the upwind engine fails on takeoff the down-wind engine (asymmetric) will combine with the weathercocking effect so you'd get (x-wind + asymmetric thrust wrking in the same direction.
Should the down-wind engine fail, the upwind engine yawing moment will be counteracted to some degree by the weather-cocking effect, ie the yawing force is x-wind minus asymmetric thrust.