Yes all toothbrushes including electric toothbrushes require toothpaste to get your teeth clean and provide you with the needed fluoride to keep your teeth healthy and strong.
I've noticed some toothbrushes that were electric that recommended using it without toothpaste but I would not use any toothbrush without toothpaste.
Just apply the toothpaste to the electric toothbrush brushes or apply the toothpaste directly to your teeth and then brush like normal and then rinse your mouth out.
You can also make a homemade toothpaste out of baking soda and water to make a baking soda toothpaste for brushing your teeth with.