Let $P$ be a square matrix such that $P^{2}=I-P$. For $\alpha,\beta,\gamma,\delta\in\mathbb{N}$, if $P^{\alpha}+P^{\beta}=\gamma I-29P$ and $P^{\alpha}-P^{\beta}=\delta I-13P$, then $\alpha+\beta+\gamma-\delta$ is equal to: