The "SAE"...are you absolutely 100% certain it is an SAE and not a CAE?
That sort of injury is fairly similar to that of a mature CAE that has attacked a slab side fish like the Gourami for the slime coat. Slab sided fish are slower moving, especially after dark when the CAE is most active.
Juvenile CAE will eat algae but once matured, they thrive on another fish' slime coat, often causing terrible wounds that do not react to treatment thanks to the infection left from the CAE and the victim dies a long, painful death severely stressed, terrified and with infection from its wounds unresponsive to any treatment.
Be VERY sure that you have not got a CAE and if by chance you have been missold one, get it out of the aquarium asap and euthanise it if the shop where you got it from will not take it back. CAE are exceptionally dangerous, vicious fish once mature.