Say " to the superpower" means that number to power of all the numbers smaller than it.
Eg. 6 to the superpower means6^5^4^3^2 which is 2388636399360109977557402041718133080829429159844757507642063199359529632522467783435119230976
What would be x to the superpower equals y to the superpower plus z to the superpower?
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.
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.