80% of your body composition will be determined by your diet.
Yes, you can eat carbs just make sure you avoid processed carbs. Processed carbs are cereals, pasta, rice, bread, waffles, pancakes, muffins, soft drinks, packaged snacks, sweets, desserts. Basically anything delicious. They're all manufactured and they're all trash. Yes, even those 12 grain breads that are oft touted as "healthy". Carbohydrate drives insulin drives fat. There's a whole bunch of science behind this but it'd make for a lengthy post so I'll save it unless someone wants me to post this information. Basically, you need to get "real" with your food and eat more veggies and eat more protein (fish, chicken, etc). Oh, and don't be scared to eat fattier cuts of meat, too. Proteins are digested slowly, don’t flood your bloodstream with glucose and then leave you sprawled out in post-carb crash. You won't be hungry within an hour which will then save you from binging.
Exercise: Don't even bother with the chronic cardio; it's unhealthy and counter-productive. What's chronic cardio? It's long stretches of cardiovascular exercise at a sustained heart rate in the 80+% range. Once you get into this zone, less fat is burned and where there’s a big dependency on glucose to fuel muscles, your body goes into a less efficient mode of fuel oxidation. Get anywhere from 30 minutes to an hour of low to moderate level aerobic movement (heartrate between 50-75%) such as walking briskly, hiking, cycling, etc. It doesn’t need to be every day, but at least a few times a week is important. Body-weight exercises are your best friend. Squats, push-ups, pull-ups, planks and over-head presses work your entire body and are far more beneficial than those awful isolation exercises. I can provide videos that show you how to do the very basic versions of these movements (wall squats, wall pushups, etc) and they also show you how to progress into doing more advanced versions of these movements. These movements will build muscle which in turn replaces fa
Unfortunately it didn't take you over-night to put on this weight so you certainly aren't going to lose it that fast either. Quick fixes are only temporary and the weight will come back.