You'd need to add an input field to select the file, then write code to upload it, then write more custom code to save it to a safe place which you've already set up on your site so it can't be accessed by unauthorized persons, then write more code to pass that file's contents to the email, and then make sure your emails don't end in a spam folder.
There's no built-in feature which sends attachments via email, so I can't point you to any example core code to follow, but those are the broad steps you'd need to consider.
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