How to Find The Amazon Account Associated With My Kindle On The Actual Device?

I have two kindles which are linked to the same Amazon account. Unfortunately, when I made my Amazon account I created a totally random email address and never thought about it again, assuming I wouldn't need it. That, as you can imagine, is not the case. I am having some problems with my kindle, and after a little research, I found a way to fix it. However, I have to sign in to the Amazon account my kindle is associated with. Well, isn't that lovely. So, my question is: is there a way to figure out what amazon account is linked to my kindles on the actual kindles or am I doomed? And if so, how?

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