Inception Auto-Root only for SM-T113 (Galaxy Tab 3 lite new edition). It works pretty much like CF-Auto-Root work. You end up with supersu installed, and it reinstalls stock recovery when done.
DO NOT USE FOR SM-T110
You void your warranty when you flash something to your device
Use at your own risk, I'm not responsible for bricking your device.
Screen flashes while installing supersu but it's nothing major
SM-T113 Inception-Auto-Root , Tool/Utility for the Samsung Galaxy Tab 3
Source Code: https://github.com/inception-android/inception_base_samsung_goyavewifi
Last Updated 2015-06-07
Thanks!!! It worked on my Samsung Galaxy Tab E T116BU (just restored the official ROM, then rooted with your file).