Well by your definition,
6 to the superpower means $$6^{5!}$$
so
x to the superpower means $$x^{(x-1)!}$$
y to the superpower means $$y^{(y-1)!}$$
z to the superpower means $$z^{(z-1)!}$$
so
I guess you are asking me to solve
$$x^{(x-1)!}=y^{(y-1)!}+z^{(z-1)!}$$
Don't know - you have me here.