Although it is very unlikely to have an engine failure, pilots are trained to recognize engine failure and how to handle the situation. Below is a situation where an engine failure is encountered during the takeoff roll for a typical B737. Prior to takeoff, the takeoff thrust is set. It’s normally around 40% initially. Then the TOGA button is pressed to make it accelerate to 90.2%-96.1%. If there’s any malfunction before 80kts, the captain will reject the takeoff. After 80kts and before V1 the captain will only reject for serious problems like engine failure or engine fire. After V1 the takeoff must continue no matter what happens. This is to prevent the aircraft from overshooting the runway when the pilot tries to stop the plane. V1, VR and V2 are calculated before every flight. It depends on the runway length, aircraft weight, outside air temperature, and everything else. So if there’s any malfunction after V1 the takeoff will continue. Nothing will be done until 600 feet above ground level. Even if there is engine fire, no action will be taken until 600 feet. Take note that with a single engine the climb will be slightly slower. At 400feet, normally the captain will choose mode HDG SEL.And at 600 feet both pilots will determine the problem and if there’s any recall checklist to be done, now is the time to do it. If it’s an engine failure, do nothing, yet.At 800 feet, set flaps up speed around 210-220kts and retract flaps 5 to flaps 1 then flaps up. After the flaps are up, LVL CHG is selected and MAX CONT thrust is set with bank angle 25degrees. After all that, the Non-normal Checklist (NNC) begins. Thrust lever is closed and engine start lever is selected to cutoff, etc. After the Engine Failure NNC, the after Takeoff Checklist is accomplished. The captain will inform the cabin while the co-pilot calls the control tower. The pilots will decide whether to continue or to come back and land. Normally, one engine is sufficient to bring the plane safely to the original destination.