Apparently when rooting and especially when S-Offing the HTC 10 users have been experiencing some issues with their radio.I believe this is due to the auto encrypt.
JCase has figured out a way to root the HTC 10 and keep your radio working. You will need to head to htcdev.com and follow the directions to get your bootloader unlocked. Then you will need to grab the latest version of TWRP for your device. Reboot into download mode and flash the new recovery. Next boot into the bootloader. Be sure to insert an Sdcard into your device for the backup. Boot into recovery. Run TWRP in read only mode, and back up all partitions except user data. Also be sure to backup system.img. Reboot TWRP recovery. download SuperSU 2.71, sideload supersu in twrp,
From there you can S-OFF your device. Even if you don't decide to S-Off your device your radio may stop working if you wipe your data after rooting since it will no longer be encrypted. Head to the link below for the steps to keep your HTC 10 radio working.
via XDA