Beta Difference

Let $X_1,\dots,X_{324},Y_1,\dots,Y_{324} \sim \text{Beta}(1,2)$ IID. Define $S_{324} = X_1 + \dots + X_{324}$ and $T_{324} = Y_1 + \dots + Y_{324}$. Approximate $\mathbb{P}[S_{324} - T_{324} > 10]$. Your answer should be in the form $\Phi(a)$, where $\Phi$ is the standard normal CDF. Find $a$.