Relative dating of intrusion
It does seem like it's impossible to know unless you have additional information. However, I think there is a hint in there. See this white halo around the intrusion? My guess (and I could be wrong here) is that it's not there for artistic reasons but rather it's there to provide a very strong hint.

My feeling that this is some kind of metamorphosed contact zone (or aureole), which transforms sedimentary rocks into their low pressure and high temperature metamorphic equivalents (shales to hornfels, limestone to marble, sandstone to quartzite, etc).

It's hard to see, but I think I can see (when zooming in ) some of the white halo extending into the bottom of layer A. That would mean A was present when E intruded, because you can't metamorphose something that's not there. Otherwise, the metamorphic aureole would be cut by layer A.



Again, I'm not sure because the image is low resolution. Maybe you should ask your teacher or if that's not possible try to figure out if you should already know about metamorphic contact zones in your stage of geological education.