I'm confused a bit. If youngsters can't (legally) drink until they're 21 how can a parent agree to them leaving home when they're 18?
The truth is that children want their parents concern at all ages; it's the suffocating control over them they don't need. In the end your child may become a better adult for leaving. My son was 17 when he left for another city to study (college) and because we were tight with money we didn't have frequent visits. At the time he wanted to go as far away from home as possible. Now, at the age of 25, still living three hours away by car, he can't get enough of us. Circumstatnces keep him away.
Of course, I was present in his life through phone calls and always showing concern. Perhaps, if your child keeps insisting on leaving (does the child have steady work?) you can arrange visits from him/her and of course tell your child how proud you are of him/her and how much trust you have in him/her. Explain that it's the world out there that frightens you.
We need to keep reminding them of our love through words and actions.
I wish you all the best and would love to share with you anything else. Good luck.