I agree with gettingrid, in that an 1800 calorie daily deficit will definitely make you lose weight. HOWEVER, this is starvation and you are going to be losing alot of muscle/lean body mass and not very much fat at all. You might not even be a very muscular person to begin with so you might think, "who cares if I lose muscle as long as I lose fat too." At least that's what I thought when I went from 240 lbs to 150 lbs in 5 months. But the thing is, now I'm a fat-skinny person because alot of the fat stayed with me while the rest of the good weight disappeared, (incidentally, now I have to gain weight in order to lose it...it's messed!) What you wanna do is create a 500 calorie daily deficit from your maintenance calories to ensure that you're actually burning off fat. Also, be consistent; don't think that just because you ate above maintenance one day that you can somehow make up for it by starving yourself the rest of the week or vice versa. Just get back on track at minus 500 cal/day as soon as possible.
As for determining maintenance, I would say just keep eating the same amount and doing the same amount of physical activity, and weigh yourself now and two weeks from now. If you are the same exact weight, that's probably your maintenance. If you've lost exactly 2 pounds, then you are already right on track for a successful fat loss diet. Don't lose more than a pound a week, (unless you're really obese, and then maybe up to 2 lbs/week.) sThink of yourself as a piece of raw meat. Now, you could just throw yourself into a 700 degree oven, and you will definitely burn really fast and maybe the insides will even be cooked. But if you want to be nice and tender and cooked all the way through, you want a to be in a 350-400 degree oven for a longer period of time.
Furthermore, make sure that 40% of your calories come from protein, 40% come from carbohydrates, and 20% come from fat. Protein: lean meat (chicken//tuna/salmon/turkey/lean steak,) eggs, whey, casein (yogurt/cottage cheese.) Carbs: Complex carbs (whole grain, oats, sweet potatoes, vegetables, beans.) Fats: Mostly mono/poly unsaturated and EFA's (olive oil, nuts, flax, fish/fish oil.) Make sure that you eat these meals spaced evenly through 6 meals per day, generally consuming protein in each meal while keeping carbs primarily in the morning and fats at night.
For exercise, make sure that you have a solid routine established before figuring out your maintenance calories, otherwise, your maintenance will be a shot in the dark. Actually, exercise isn't even necessary for fat loss, but it is extremely helpful. A good routine will consist of 3-4 days of weight training per week which should be the primary focus. Once you've established a good weight training regimen, then look into cardio. High intensity interval training (HIIT) is the best, but you can look up the specifics on your own.