For relation $T$: if $(a, b) \in T$, then $a^2 - b^2 = I$ where $I \in Z$.
Then, $(b, a)$ on relation $T$ means $b^2 - a^2 = -I$.
Since $-I \in Z$, $T$ is symmetric.
For relation $S = {(a, b) : a, b \in R - {0}, 2 + \frac{a}{b} > 0}$, $2 + \frac{a}{b} > 0 \implies \frac{a}{b} > -2$.
If $(b, a) \in S$ then $2 + \frac{b}{a}$ is not necessarily positive. Therefore, $S$ is not symmetric.