Asymptotic Runtime of Interrelated Functions
Here is one approach.  Plug in the definition of $T(n)$ into your first equation, and we get

$$S(n) = 2S(n/4) + S(n/8) + 2T(n/8).$$

Now plug in again and we get

$$S(n) = 2S(n/4) + S(n/8) + 2S(n/16) + 4T(n/16).$$

Keep plugging in and eventually we get

$$S(n) = 2S(n/4) + S(n/8) + 2S(n/16) + 4S(n/32) + 8S(n/64) + \dots + O(1).$$

Now solve that recurrence relation for $S(n)$, noting that now you have a single function (you don't have two interrelated functions any longer).