[sokoloff]

I have no first-hand information, but I think this is going to turn out to be a reduced thrust takeoff with the crew being unaware of that (meaning they screwed up).

Airliners have enough power to lose an engine at a decision speed (V1) while still on the runway and on the one remaining engine continue to accelerate on the runway to rotation and eventually liftoff speed and still clear obstacles. There is no mention of an engine loss causing this issue (and surely the airplane wouldn't launch for FL360 with one engine INOP), so this almost has to be a mis-set takeoff thrust accident as, with both engines set for proper takeoff thrust, it's rare to use more than 2/3 of the runway and the initial climb is brisk due to the large excess of power a turbojet engine has at sea level.