To explore Darjeeling 4 days is much needed. The cost for solo travel to Darjeeling comes between 15k to 25k. Based on mode of transport and place you stay the cost varies. To reach Kanchenjunga from Darjeeling via Yuksom by road it takes 4 hours. Then you need to trek to the peak. Looks like solo trek is not advisable for many say permit is not issued for solo trekkers. So if you plan via a group or via a guide cost varies accordingly. You need to check in the permit Center there. Will share a few tripoto links written by travellers pertaining to their travel to Kanchenjunga see if it is suitable for your travel. https://www.tripoto.com/india/trips/land-rover-and-kanchenjunga The beautiful sunrise of Kanchenjunga
https://www.tripoto.com/trip/the-beautiful-sunrise-of-kanchenjunga-2470 For the love of Kanchenjunga
https://www.tripoto.com/jammu-and-kashmir/trips/for-the-love-of-kanchenjunga-5af558e80fd21