Ahhh, I see yes that would be a little bit tricky.
I was assuming you each had separate profiles on the whole computer, I forgot about OE having having the switch identity thing.

Well if in the future you want to try again or if OE is messing up again there are a couple ways around the identity thing.

Either set up 2 Tbird accounts - 1 for each of you and give them a name {rename the icon} so you know which is which. like Alans email & Mels email

Or set it up like I have on my computer-

What I did on my computer is set up separate User Accounts in the control panel for each of us - hubby, daughter, boys and me. There's also a Guest account if you have anyone else that might use it.
The welcome screen opens up and we each have our own icon to click and then log onto, you can have a password or not.
I log on to my account/profile and they can each log on to theirs.
I am the administrator for the computer, the others have limited accounts.
That also keeps anyone from making problematic changes or deleting anything of mine or messing up the computer.

So if you did that your email would only be on your side and his would only be on his side.

Anyway that's a whole other topic LOL