I've been where you are and biking was a big part of my program; commute to work by bike and then do long trips on weekends. If you can work yourself up to 70 mile days a couple of times a week, you can lose any desired amount of weight, especially if you do that in the summer.
280 and 250 are pounds?
In which case I am 314 and my goal is about 210.
I think I just need to decide to do it.
In 1999 I went from 343 to 202, in about 5 months.
I began walking, after work, every night, once I hit 5 klms (say 3 miles) things began to improve and I doubled it. Then I bought my first ever in my life bike. I was 40. I began slowly, rode much further than I ever walked, within a month I was riding 30 klms, (18 miles) before work, eventually it was 80 klms, - 50 miles the or 4 times a week, still walking and swimming then I took up roller blading. As the weight drops it gets easier to exercise. I kept the weight off completely for about 8 years, then gradually put it back on, the past 5 years have been bad. My best tips are, start your trip riding into the wind, makes an easier trip back, and every calorie you don't eat, is one less you have to burn off.
I would start my rides on empty forcing my body to consume fat, stay hydrated, and withing 20 minutes of finishing a long ride, consume some lean protein, even an egg white in a glass of milk, so you have something to repair strained muscles with. You will do it.
Yay! Welcome to the cycling fold!
PS: I bet you can do much more than ten miles. Bikes are seriously efficient machines (massively more so than cars) and cycling is a whole load of fun - most people who take up cycling find they do more miles than they thought they could for these reasons