The Xbox 360 console might present an E10 error code in the case of Hardware Failure. It is not known for sure what the cause of the E10 error is, but there is speculation and some information online that can be helpful in diagnosing it. It presents as an on-screen message that instructs the user to contact Microsoft Customer Support. In addition to the on-screen error, the console is also usually blinking a single red light in section 4 in the ring of light on the console (as shown).
Information available online suggests that the E10 error may be caused by poor connection of the CPU to the motherboard, such as a cold solder joint or bridged solder joints. If true then it could have been caused during the manufacturing process, or as a result of overheating. Another potential problem is the X-Clamp holding down the heatsink, which might have caused the board to warp under excessive heat and disrupted the connection to the board. This however, is only speculation and a user should contact Microsoft Customer Support and seek help.
The error code associated with E10 is 0022. To get an error code from an Xbox 360 console that is displaying an E10 error (or 3ROL) you simply press and hold the "sync up" button (used to connect wireless controllers) and then press the Eject button for the DVD drive. This will bring up the first digit of the error code (usually it is all four lights blinking red, which represents 0, not 4). With the sync up button still held, press the Eject button again and you get the second digit. Do this twice more to get the full 4 digits of the error code.
For more information on the error code you receive, or on Xbox 360 hardware problems in general, read this Xbox-Scene forum thread.