Comment by avalys
Every multi-engine airliner is designed to be able to take off safely even if an engine fails at a critical moment. What might have happened in this case is that the mechanism of failure of one engine caused damaged or interfered with the operation of another engine (via smoke, debris, etc.), and taking off with two engines degraded is not part of the design criteria.
Some engine failures can't be contained within the cowling, like turbine disc rupture. Probably something like this happened where fragments punctured the surrounding wing structure and/or fuel tanks.