Three positive integers P, Q and R, each with no leading zeroes and having more than one digit, are such that:

(i) Q = P + sod (P), and:

(ii) R = Q + sod (Q), where: sod(x) = sum of the digits of x, and:

(iii) The digits of R are obtained by reversing the digits of P.

Determine all possible value(s) of P, that satisfy the given conditions.

Note: While a solution may be trivial with the aid of a computer program, show how to derive it without one.