Applying differential cryptanalysis to ciphers with addition mod $2^{32}$
This is called an Even-Mansour cipher.

Actually, for the differential cryptanalysis it does not matter what sort of difference you use, you only need that it propagates deterministically through linear transformations  (whatever linearity means). In this case you use a difference modulo $2^{32}$:
$$
A \boxminus B \equiv (A-B)\pmod{2^{32}}.
$$

You compute the differential distribution table for $S$ in the same way, but replace $\oplus$ with $\boxminus$.