Sending smtp email from microcontroller
OK, so in order:


To send an email, your equipment needs to have an SMTP conversation with a mail server somewhere.  In this conversation, your system will be a client to the mail server.
SMTP is a protocol which runs on TCP, not UDP.  There's no simple UDP equivalent.
The very simplest way to understand SMTP would be to look at RFC821, which is very, very old and has been superseded, but still describes the basic principles correctly.
TCP is much, much, much more complex to implement than UDP (like a month vs an hour), and if you're struggling to comprehend the SMTP rfcs, you'll find TCP very difficult indeed.


In general, if I need UDP/IP, I just write the code to do it, and if I need TCP/IP, I use someone else's stack (often LWIP on small processors).

Do not make the mistake of thinking TCP is 'some extra effort' vs UDP, it's not at all like that, and is a very big 'some extra'.  If you want it to work at all reasonably in the face of the packet loss which you get on WiFi, you need a decent implementation, not just the most basic SYN/ACK stuff.

My advice: start with lwip - if you can't get that going, then you're probably not ready to write the rest of it yourself anyway.

Update: Make sure you see Dave Tweed's comment below - I had not realised that your module had a complete TCP/IP stack in it already - you basically just need to work out how to send and receive lines of text over TCP with it, then you should be able to work through RFC821 (and its successors) to send a message.