It's not possible to do this with the out-of-the-box Confluence tools, but you can export pages (amongst many other things) with the Confluence Command Line Interface add-on. Assuming you're on Windows, you could use Powershell (a built-in Windows tool) to watch a folder, and every time a file appears in it (in this case an exported page from Confluence), mail that file to a specific address and move the exported file to an archive folder. Alternatively you could tell Powershell to take the contents of a folder and mail them to an address on a regular schedule, say once a day.
This might be overcomplicated and a much simpler answer may well be available though.....
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