Hey - seriously it is absolutely possible to go away pretty much anywhere in the world when you are under 18. Many, many people I know, myself included, have gone on clubbing holidays at 17 or even younger.
Basically, most of the big companies e.g Thomson, Thomas Cook etc will probably require one of you to be 18.. or even both of you.
However this should not stop you as it is often cheaper to book the flights and hotel seperately. Booking flights with companies such as Easyjet is not a problem if you are aged under 18. I think you might be allowed to fly alone at 14? Have to check this out.
I would then suggest booking the hotel seperately, through any number of sites but I have found Travel Republic to be excellent. However, before you book, ring up the hotel and check their policy on under 18's. Websites might let you book if you are under 18 but you have to check with the hotel personally to be safe. In the past we have rang hotels and a couple have said no but most say it is fine, especially in places like Aiya Napa, you can then go ahead and book the hotel and flights with no worries.