If you are given ΔH for this reaction which occurs at constant pressure, what additional information you need to determine ΔE?
Because:

1) your question assumes that the volumes of the solids ($\ce{Al}$ and $\ce{AlCl3}$) are negligible compared to the volume of the $\ce{Cl2}$ gas. This means that $\Delta V \approx V(\ce{Cl2})$.

2) your question assumes that chlorine gas behaves ideally. This means that $V(\ce{Cl2}) = \frac{nRT}{p}$.

In the end, it means you only need two of the three variables ($p$, $T$, $V$) in order to obtain all the information you want.

I would however be very careful about using molar quantities, in particular $V_m$ (since $p$ and $T$ are intensive properties), if the question is asking you to find $\Delta H$ and $\Delta E$ in terms of $\text{kJ mol}^{-1}$.