This isn't perfect, but it will work. You can use your email server(s) as the synchronization tool.
It requires you to check you email via both computers at least every 10 days (depending on what you set).
Simply set up each computer's Outlook Express to collect email, and on the account settings, set it to leave a copy of the mail on the server, and set it to delete the mail once every X days -- the period during which you will need to go to the other computer to check the email. You will end up with all your email on both computers.
As far as your sent email, for each email you send out, send a BCC to yourself. Set up a rule for incoming mail, where it places any mail sent from yourself in the "sent mail" folder... You won't be able to tell the difference between mail sent from that computer or the other one.
There are a few minor drawbacks (like not being able to flag mail as read, and having a bit of a email backlog on your server), but it is probably the easiest way to get all your email on both machines.