what I want to accomplish is adding 20 pounds of muscle and to lose 10 pounds of fat that would put me around 10 to 12% body fat
First and foremost your goals are entirely unrealistic unless you are getting anabolic assistance or are a complete newcomer to weight training(or coming off of a long layoff). The 20 pounds of muscle gain in 10 weeks itself is going to be tough, let alone trying to burn fat along with it. Adding 20 true pounds of muscle mass in 10 weeks is hard enough
with steroids once you take into consideration how much of your weight gain is fat and water. 20 pounds of muscle is
a lot of muscle any way you cut it. Just don't get your hopes up on that goal as it's pretty far out of reach unless as I said you are a newcomer in which your body will be primed for growth.
As far as your cardio question there is no one correct answer. As burning said you don't even have to do cardio to burn fat. I successfully dieted down this spring using only weightlifting and a reduced calorie diet. It's quite simple, if the caloric deficit is there and you're weight training, then you will lose fat while retaining muscle. It may not be as fast as if you added cardio, but speed in weight loss is not always the best way regardless how bad you want it. Anf the faster you lose the weight the harder it will be to maintain the level you reach. Period.
I have anything but great genetics when it comes to fat burning. In fact I was pretty damn fat a few years ago, but with a finely tuned diet and a simple 3x per week weight lifting schedule the fat melted off of me. Cardio may have sped it up some but it also may have caused a loss of more muscle mass which would be a bad thing for me. I intentionally didn't do cardio on my last diet to test my theory and it ended up being true.
Truthfully I am a lazy ass when it comes to cardio, at least when it is intended for fat loss. I know it is not required so I feel there is no need to do it. Now if you're motivation is to improve your cardiovascular condition, or you just enjoy doing it, then it's great.
Also if you truly want to maximize fat loss I would recommend doing wind sprints on days you don't lift weights and then do lower intensity cardio on your workout days. High intensity cardio burns more calories in less time and helps speed up your metabolism which is a good thing. If I go back to doing cardio someday, which I probably will, I will most likely do wind sprints on off days and do no cardio on workout days. This is the best of both worlds.