There was an interesting article in the US AOPA mag about Engine
Failure At Take Off situations. It could be applied to EF at any altitude but likely your speed will be higher.
The first thing that should come as an automatic response is to unload the wings.....push forward hard. The article makes a point of stating how much you actually have to push, and the amount of horizon which fills the screen - it varies for each aeroplane but rule of thumb is that you go from 2 thirds sky filling the screen (on climb out) to 2 thirds ground filling the screen (at best glide).
The reasons for this are (amongst others)
a) when the wings are unloaded in the push over, nothing bad like stall / spin can happen and it gives some extra time to think about things. A pilot faced with EFATO is likely to be caught off guard and an automatic response like this could save a life or two.
b) You need to increase airspeed by sacrificing height, there is no other way around
Good article......