E82 Error Code has been a common error on the slims for some time since release, E82 error is the GPU has overheated and come unseated from the main board.
Try to turn the console on without a HDD in place. The HDMI cable also may be a reason so try to use a standard AV-cable. If the console still displays the error, then you may have to reflow/reball the GPU. Also, check with MicroSoft and see if it is still covered under warranty.
Hope this helps, good luck.