But f(x) = eml(1, x) and g(x) = eml(x, 1) are different operations. What operation are you saying is supposed to be its own inverse?

eml(1,eml(x,1)) = e + x

and

eml(eml(1,x),1) = e^e * x

Okay, I’m tired. Not quite inverse but per the title , must be a way.

I was mistaken above in the first identity, it is

eml(1,eml(x,1)) = e - x

Which then if you iterate gives x (ie is inverse of itself).

eml(1,eml(eml(1,eml(x,1)),1)) = x