I used an example from my current position when a girl was very poorly and had to take time off work. I'd had this experience previously when a family member passed and had to take time off myself, so could empathise with her when she returned to work and was still in recovery and didn't really want to be there. It was quite a hard question to answer but I think I managed in the end.
If you could somehow measure the type of words in the emails, such as whether or not some are considered angry words or something, then you could answer the ones with more angry words first. You could also rank them in the order of stuff that only you, due to your specialized skill set, can answer, and also the number of emails from the same person, perhaps also showing or highlighting frustration, and therefore should be addressed first.