Using regular laundry detergent in your High Efficiency washing machine won't harm the washing machine however if you do use regular detergent in your high efficiency washing machine instead of the detergent that is made for high efficiency washing machines then the soap won't be rinsed out good enough from your laundry.
The laundry detergent made for High Efficiency washing machines is made to create low suds where as regular detergent creates more soap suds which makes it hard to get them rinsed out of the laundry in a high efficiency washing machine.
So to get good cleaning results always use the detergent made for high efficiency washing machines.