GreyBeard,
I also have not been able to find data on the 109E4/N. However, in Warplanes of the Third Reich page 550, William Green wrote that the performance of the 109T-2 possessed a performance closely comparable to the 109E4/N.
Follows is Green's performance for the T-2:
(Weight 6173, and emergency power, speed in mph)
Sea Level 304, 3280 feet 317, 6560 feet 328, 9840 feet 339, 13120 feet 351, 16400 feet 354, 19685 feet 357.
Green did comment that the performance was similar even though the T-2 had a longer wing span and greater area.
On page 552 Green wrote that the E4/N had an initial rate of climb of 3420 feet per minute, and reached an altitude of 16400 feet in 6.1 minutes. The E4/N could gain 1970 feet in a combat turn at an altitude of 3280 feet. Turn time for the E4/N at 3280 was 25 seconds for a 360 degree turn. Unfortunately, the weight of the machine was not given.
This is the only data that I have found on the E4/N
Eagledad