S(x) denotes the sum of squares of the digits. For example:
S(97) = 9² + 7² = 130.

Find all possible positive integer values of N < 2014 such that:
N ^oF= (S(N) - 5) ^oC

N.B.: F = (9/5)*C + 32

*** As an extra challenge, solve this puzzle using a non computer program assisted method.