New To the Site, Could Use Some Advice

Hi everyone!
After about 6 years of being unhappy but feeling too busy to do anything about it, I've finally decided to step up and take care of my weight.
I've been doing the tracking for about a week now with a daily calorie goal of 1320.
I have also been doing an hour of cardio daily 5 days a week (elliptical 3 days and bike 2 days) and I've been doing weight training 3 days a week.
Here's where my questions come in: When I do elliptical, it gives me about 900 extra calories (bike gives me about 700). Am I supposed to be eating all of those calories back? It seems kind of weird to work calories off and then just eat them back. And, I have to work out after work, so usually 4-5, so then I end up with 1,000 calories that I'm supposed to for dinner, which just seems crazy. I haven't eaten ALL of my calories for the last week because it's just so many! I've been netting around 7-800 a day.

Just wondering what other people's opinions are on this situation. Thanks guys!