I'm trying to figure out how keep my metabolism up

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I've been overweight for decades and would love to figure out how to eat just a little less daily so that I could loose weight. I've used the calculators to see my BMR and my tdee. I've joined a gym so that I can learn how to slowly build up my strength without damaging myself. I enjoy being outdoors going for walks , beekeeping and gardening. Just figuring out how much to eat is the unknown.
I am in a team to loose 10 pounds in these next 10 weeks. So today 'mI eating just fruit and vegetables to see if I can loose the pound or two I need to loose before weigh in on Wednesday.