eml(1,eml(x,1)) = eml(eml(1,x),1) = exp(ln(x)) = ln(exp(x)) = x

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