Fasting is fastest. Just drink water for the next 6 weeks and I guarantee you'll easily have lost 7-10kg. Possibly 3 times that if you have plenty to lose. Of course any diet is only as good as its compliance. However there's something to be said for keeping it simple. And if approached correctly it's not necessarily unhealthy. There's plenty of people to swear by all the other diets being advocated, and you need to decide what you can stick to, but simply to present an alternative without necessarily recommending it here goes:
I'd spend the first week cleaning up the diet, ditching the addictive foods so you can get the withdrawal out the way so lose the coffee and grains and wind back all carbs while eating really big steaks with eggs and bacon. This'll be when you can adjust your water needs as well as you'll stop retaining as much. As others have said, that's probably half your problem right there. Then stop eating. A week may be enough depending on whether you're heading for 7 or 10kg, but 2 weeks will be better. You want to end up a few of kilos below your target so you can just monitor that if you like. It's not impossible to go for 3 weeks. At the end of the fast, you're going to take at least a week with bone broths, poached eggs and small portions! A few days to get your digestion back up to speed before trying anything too challenging, and even then you're looking to eat meat. If you fasted 2 weeks then you'll probably find that the remaining 3 weeks is plenty to get back up to speed so take your time and avoid getting sick. You'll be gaining weight back as soon as you start eating so don't panic. Don't over-exert yourself during the fast, but feel free to walk as often as you can.
Almost certainly unnecessary and certainly a challenge but it's really that important and you're motivated then it's kinda hard to go wrong on the weight loss. You do need to watch out for other risks though.