sod(x

^{2}) - x = 2, where sod(n) denotes the sum of the digits in the base-10 representation of n.

(II) Determine all possible values of a base-11 positive integer y such that:

sod(y

^{2}) - y = 2, where sod(n) denotes the sum of the digits in the base-11 representation of n.

In each of (I) and (II) prove that these are the only respective valid value(s) corresponding to x and y.