Suppose there is a random variable $X$ that is conditioned on an event $E\in\{0,1\}$. I am looking for a proper way to express this. For example, let random variable $Y=T+X$, where $T$ is another random variable (independent of $E$). Can I write something like this (which seems rather strange)?
$$Y_0=T+X|E=0$$
Unfortunately, in my actual expression, $X$ has both a subscript and a superscript, so I can't use those without some awkwardness. Any ideas?