XOR constraint representation

In an scheduling optimization problem, for job $l$, $\xi_l$ is binary variable that $\xi_l=1$ shows job $l$ is selected. $t_{r,l}$ and $t_{e,l}$ are registration time and time that job is completed. Also, each job can wait for $t_l$. In this problem, one contrarian disallows any parallel activities. This constraint is XOR: \begin{align} &\begin{cases}T_{r,l}+t_l\geq (\xi_l+\xi_{l^\prime}-1)(T_{e,l^\prime}+t_{l^\prime})\quad\forall l\neq l^\prime\\\hspace{3cm}\text{xor}\\T_{r,l^\prime}+t_{l^\prime}\geq (\xi_l+\xi_{l^\prime}-1)(T_{e,l}+t_{l})\quad\forall l\neq l^\prime\end{cases} \end{align} How can I merge these two part in one (linear form) constriction? Can I represent this constraint using other equation?