Generally speaking, both tires on any one axle should be the same load range and tread, and inflated to the same pressure.
It may not make much difference on a trailer, though.
Keep in mind that you may not be able to inflate the E tire to the max sidewall pressure, as some will say you should; the rim may not be built to handle that much pressure. Inflate the tire to get the best contact patch with the road surface. No, inflating the tire to a lower pressure will not damage it. Remember, the Jeep Wrangler Rubicon came from the factory with Load Range E tires, inflated to 33 PSI for normal use, 12 to 15 PSI for off road. The tires survived quite well!
