Hello Dan,
Thanks for reaching out!
Our plugins do not have any invoicing functionality built in. You would need to rely on an eCommerce solution (WooCommerce or EDD) to do this for you.
If you use any of the above you can still set up tickets and sell them, while WooCommerce (and possibly an add-on to that) will take care of creating and sending the invoice.
Or you can set up WooCommerce products to be your tickets without having the need for our ticketing plugins. Maybe it would be simpler.
Let me know if you have any further questions.
Cheers,
Andras