Oof, that's a bad injury indeed.
Looks like the tank mate tried to take a bite. It happens. Even if your tank is big enough with enough hides, it can happen.
First things first: separate them. The injured axolotl will be weak and vulnerable right now and that means the likelihood of another injury happening is bigger. If you have a big enough tub or spare tank, put him in there.
Second: keep it clean. Axolotls are amazing at healing injuries, but an open wound like this is still vulnerable. Clean water, clean tank; preferably no substrate. Be much more vigilant with keeping the water clean than normally.
That should be enough. Keep an eye on it, of course. It's likely the axolotl will have less appetite the coming days, but that shouldn't take too long.
Watch out for fungus as well.
I'm not a big fan of fridging. It's great in preventing situations from getting worse, but it also slows down... well, everything, healing included. That means it's less "risky" than keeping the injured axolotl in a room temperature tank, but it also means he's going to be in there for a few weeks, which comes with its own problems and issues.
Once the wound doesn't look so "open" anymore and the axolotl is back to its old behaviour it should be safe to put the two back together. Be sure not to blame the other one too much; accidents happen
