A service like Protus Fax will do what you want, and you don't need a phone line.

All they do is issue with a number for receiving faxes (which just arrive at the designated e-mail account), and a password which you put at the top of any messages you wish to fax. As it supports MIME attachments, you could easily automate sending with MIME::Lite or similar.

I can't help you with receiving faxes, beyond saying that Protus sends them back as TIFF. We have ways of making TIFFs more friendly ...

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