Yes, it is possible to do Everest Base Camp Trek in 10 days but possible with helicopter fly back from Everest Base Camp. Otherwise, it takes at least 12 days to accomplish your ebc trek. If you have got 10 days to spend Nepal and willing to do EBC trek and you are all set up, you can follow this itinerary with helicopter fly out from Kalapatthar/EBC.Everest Base Camp Trek 10 days with helicopterDay1: Arrival in Kathmandu 1,320 m and transfer to hotel.Day2: Day 3 Fly to Lukla/2840m, Trek to Phakding 2,610m/30 minutes flight 3 - 4 Hours trekDay3: Trek to Namche Bazaar 3,440 m / 11, 350 feet - 06 hrs.Day4: At Namche for acclimatization and short scenic hike up to Everest View Hotel ( 3880m)Day5: Trek to Tengboche Monastery( 3,867 m) - 05 hrs.Day6: Trek to Dingboche 4,410 m / 14,470 feet -05 hrs.Day7: At Dingboche, rest day for acclimatization.Day8: Trek to Lobuche 4,960 m - 05 hrs.Day9: Trek to Everest Base Camp 5,364 m and Back to GorakShep - 07 hrs.Day10: Climb Kalapatthar 5,545 m, and fly to Lukla on a Heli and Fly to Kathmandu with regular flight - 04 hrs.