One: A person finds a letter somewhere in an old apartment building / house . He / she reads it and find that it was addressed to a previous tenant // owner and he / she decides to send a letter back anyway. The one who receives it could either be the original sender or a distant relative (descendant) of the original sender. It could have been read for the first time years after it was sent.
Two: A student finds a little note stashed in between the pages of an obscure book. Something about it intrigues him / her. The note tells them a bit about the writer and it gives instructions on where to put the "reply" note. So, these two students begin to exchange little notes to each other in a huge library used by many other students. They can even tell each other their email addresses.
tab SUBPLOT They despise each other in real life. However, since they actually get a chance to know each other through writing each other, they feel they can be friends with the other person, not knowing they are enemies.
Three: We can base it on "A Cinderella Story" where they randomly meet at an online chat room and just start talking to each other. They find they go to the same school (could be a college or university) and decide to meet at a masquerade ball?
All plots could be charming and serendipitous, either way, it would be up to us if we'd actually want these two characters to meet or not. They can exchange short and quick messages just like in actual texts and chat, but still, no text talk.