Can a 2 engines plane takeoff at MTOW when 1 engine quits,or only at lower weight?

[Pugilistic Animus]

In the scenario described if Max ToW is equal to the RTOW then the plane would be ok to takeoff provided appropriate WAT limits apply for the following
1. Obstacles

2.second segment critical climb

On a particular runway
WAT limits for the ASDA, TORA and TODA and NTOFP must be met if they are, then RTOW can match MTOW