You'll cope, OP. I remember dropping DD1 off at uni for the first time. I felt heartbroken leaving her. Everything was empty without her. I came home and thought "that's it, all my happy times are over".
It was fine. It took me a week or so to adjust, but it was fine. At the beginning I kept really busy. I caught up with lots of friends when I wasn't working and did loads of stuff with DD2. And there ended up being so many positives.
I had more time to catch up on friendships and the initial loneliness made me make more effort. I had more time for DH and we started going out as a couple more - there was nothing stopping us before but it really made me throw myself into my life at home. The house was so much tidier and I couldn't believe how much less work there was, less washing up, less clothes washing, and I was able to cook with one less person moaning they didn't like it!
I made my mind up I would do stuff for me so I was occupied and not dwelling on it. I don't know if you're full time working but if not fill some extra time. I work 3 days a week and I increased to 4 for a bit, plus I redid my maths A level, have since re-learnt German (these were both things I did quite badly at at school through laziness/ partying/ boys) and have retaken up singing lessons and joined the gym. These things wouldn't be to a lot of people's taste (!) but you get the gist. I'd strongly recommend thinking of something you can do that's just for you.
I got much closer to DD2 as a result and that has lasted. I had time to spend with just her. She herself is now at uni but the bond we forged in those years has held us in really good stead.
And here is the bit I didn't expect - I got closer to DD1 too. It's something I've seen happen with other friends and their uni age offspring too, so not just me. Away from living under your roof, they start a much more adult to adult interaction with you. I loved hearing about uni life. She usually texted to moan about work or when there was a friendship issue/ gossip, but that was fine. If I texted her I didn't expect or demand any kind of instant reply and if it was a few days before I got an answer I would just act beeezily as if it was 5 mins later. I think this was key - I never berated her for his long she hadn't been in contact, just was pleased and interested to hear from her and I think that meant she always felt she could chat. Then, if she's near enough, you'll be able to visit now and then and you get a whole new adult relationship. I used to occasionally go up on a Sunday if she was at a loose end, or stay for a night if her friends went home for the weekend and she was alone. I honestly had some of the best times ever then and still miss those days (she finished last summer).
Now, having insisted she would stay in uni town and never come back, she suddenly moved back into home and now has moved boyfriend in with us too. This is a whole different set of problems! It was honestly much better for our relationship when she was living away - having got this lovely adult bond I now feel she's reverted back to a teenager again and it's as though I have a 15 year old living at home along with equally immature boyfriend. But that's for a whole different post. My point is, enjoy this stage in your life while it lasts. Parts of it will be better than you ever imagined.