There was a story this morning about how normal people find a constant flood of emails very stressful because it is constantly interrupting whatever they are doing. As someone who has been emailing since 1987 (with a six month break), I find dealing with it less stressful than phone calls and desk visits because you can leave it until later.
It is definitely true that being interupted whilst trying to concentrate on some tricky piece of work can be somewhat stressful (and it is cumulative). One aspect that was not mentioned is that you have to discard everything you were thinking of and bring some other subject to mind; not always the easiest thing to do especially if you are deep in concentration.
Of course it is also unavoidable, and not always unwelcome. But back to emails,
Don't read emails when they arrive, and if you have a ping that announces each email that arrives, turn it off. Check your inbox regularly – on the hour, every half hour, or even every 15 minutes (although that is perhaps too frequent for when you are concentrating on something). You can change the frequency based on what you are doing – if you're concentrating on a project or for a deadline, check less often.
The point is you choose when to deal with emails.
Another source of stress is the amount of emails in your inbox; your inbox is not a "todo" list. Create a "todo" folder and move emails from your inbox into it, and concentrate on keeping that folder reasonably well processed. Your inbox becomes a cesspool of spam (there's always some that gets through), near-spam, and general information. Of course you can get much more organised than this!
And make your own decision on the priority of tasks given through emails. You may agree with the priority a sender sets on a task, or you may disagree, but you decide.
Ultimately the more control you take over your email, the less angst it causes you.