I am building a basic support request system where the customer can log in and ask a question and an admin can go in and reply and it will set the status to \"Responded\" an
When sending the email to the user you can have it sent from an email address created for that specific ticket. Something that can identify it with your email system to help you route it back to the php ticketing system.
support(ticketnumber)@domain
support12345@mydomain.com
Then it depends on your email server how to go from there. There are several useful tips at this question that may help or get your started.
How to get email and their attachments from PHP