10 pounds in a month is certainly possible, especially with a trainer, but not easy. Remember the formula is 3500 calories down will lose you 1 pound... this includes both training (additional calories burned) and eating. So if you want to lose that kind of weight, doing the math you need to either excerise off or eat 8000 calories less per week. That's quite a few; especially when your intake was probably somewhere between 1800 and 2000 before.
Odds are if you're at the weight you're at, you probably have been taking in far more calories than you think. A safe rule of math, btw; is you should never really take in less calories than your body weight (in lbs) X 10 over an extended period; and really X 11 is about right (X15 would be your standard "break even", so if you weigh close to 140 at this point you could eat ~2000 calories per day and be semi-active and maintain your weight).
This is where this is tool is truly starting to help me. I realized I had been taking in ~3400 calories, which is why (similar to you) I had gained about 12 pounds over the last year and a half (since my workout partner had a baby and stopped working out with me). I also hadn't been working out enough. I also got an addiction to sugary beverages (specifically Starbucks Frappucino's and Fat Free Whip Free Rasberry Mochas... 200 calories per drink X ~4 a day adds up), and I randomly snacked a good bit.
Being consious of what you eat is a GREAT start. Cardio should be the crux of your focus but don't forget the muscle work (if you have a good trainer they'll take care of all of this for you, but the bottom line is if you cut that many calories and don't do serious muscle work, you'll burn your muscle frame and weigh less but still not look any better).
Whew! Just some advice; while I've only been "back on dieting" for a week (I look good, but a little bit is "starting to form" on my tummy area, and I don't want it to expand. Plus I got in a bet with some friends :)), I've previously had two other phases (one about 12 years ago when I lost 50 pounds, and one 3 years ago when I lost 20; every now and again I just "slip" and have to get refocused). On this week I'm already down 4 pounds. There is straight science and math in losing weight; don't fall for some of the fad diets people want to do, shortcuts never work for anything in life. Just eat healthy, track your calories on here, and work well with your trainer, and you'll hit your goals.