Well, the math is really easy.
With OEI, the thrust of the broken engine is replaced by its windmilling drag and their sum (thrust from the surviving engine + drag from the inoperative one) generates a yaw moment which is counteracted by the rudder:
Picture from this report, drag D added by me
At pre-design phase, the lateral placement of the engines also takes this condition into account.
When the engine not only fails but completely detaches from the wing, the situation becomes easier by the point of view of the yaw since now the rudder must compensate only for the surviving thrust. Anyway now we have a side of the airplane which is lighter than the other and the lift on that side must be lowered (i.e. increased on the other side) to avoid a roll: an aileron input (or an asymmetric flap/spoiler deployment if possible) is now needed as well.