Eating back burnt calories? Still lose weight?

Do you need to eat back your burnt calories from exercise?

If I want to lose weight, Iam supposed to 1200-1300 calories but when I go to the gym I end up burning about 500 calories come home and am so hungry! that I eat 1800 for that day...will I still lose weight?

Also how do I calculate how much I need to eat and burn if I want to lose 0.75 kg per week?
Eating back burnt calories? Still lose weight?
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