In reply to goldmember:
It's definitely possible, but won't be easy. You'll need to work extremely hard, eat quality food with plenty of protein, eat only just enough and maintain commitment to your goals for long enough to see results.
Exercise: generally, explosive workouts will yield the greatest bang for your buck, prompting an increase in post-exercise metabolic rate (and thus burning fat) without inducing muscle catabolism (as long steady-state sessions are wont to do). That means performing maximal effort sessions over a variety of intervals from very short bursts of heavy resistance (e.g. Olympic lifts) to somewhat longer intervals using lighter resistance (e.g. Tabata sets, minute on / minute off sprints).
Big, 'real-world' movements are the ideal - avoid the bodybuilding ethos of isolating muscles as far as possible. Also be aware that you must not start hauling on big weights without learning appropriate form. Weightlifting properly is a skill, and many aspects are not intuitive. Youtube and sites such as Dragon Door, Bodybuilding.com can be a rich source of info, but far better would be some coaching from someone appropriately qualified / experienced. Further, intense exercise releases big quantities of endorphins which may mask pain; be careful to listen to your body and stop at the first sign of injury.
Diet: research seems to suggest one can fend off catabolic damage and support tissue repair with sufficient intake of protein within 30 minutes of session ending. You'll want some protein shake, as it's cheaper than meat / eggs etc. and of appropriate physiological quality to be readily utilised. That said, a study I saw recently suggested that the timing of protein intake is far more important than the nature of the protein.
Some folk are having good fat loss results using the 5:2 diet. Anecdotally I use it myself: my fitness goals are somewhat different to yours as I'm currently focused on increasing CV endurance. Despite significant weight loss over the 3 months I've used it, my peak strength hasn't decined significantly across a variety of movements and body fat is considerably reduced (now estimated at approx. 10%). What the research says on this I'm not sure. I know it's working well for me, and I have no problem training on 'fast' days.
Be aware that with your aim in mind, weight loss per se won't be a useful guide as to your progress. If you can, go to an exercise physiologist who can take accurate body fat measurements using calipers; you can then compare results reliably over time. Better yet, such a person will be able to offer useful advice on how best to achieve your goals. Alternatively and more cheaply you can get some useful data from periodic hip, waist and neck measurements.
Although I have reservations about some of the organisation's literary output (a bit dogmatic in some instances to say the least) I would think CrossFit might be a good place to start for you. Ensure the instructor pays adequate attention to promoting the concept of good form, particularly when lifting weights. If they don't, walk away. Good luck!