Perhaps,
lomapaseo, BOTH reports
are correct:-
"
A passenger plane, trailing smoke from its left engine..", and,
"
Gardiner had recalled that while the aircraft was climbing to 350 feet after takeoff, the right engine lost power....
You are indeed correct when you say,
the engine manufacturer’s examination is going to determine... the health of the engines
An aircraft with a sick left engine, and the power "lost" on the right would almost certainly be the ingredients needed to cause loss of flight capability.