From the Wikipedia, E-D nozzle works similarly to aerospike nozzle which compensates the exhaust gas in the atmosphere to increase specific impulse.
From Hill & Peterson, "Mechanics and Thermodynamics of Propulsion", 3rd printing, November 1970.
I summarize from the relevant portion of Chapter 13, Chemical Rockets: Expansion in Nozzles (pp 413 & 414):
- ...the presence of a free jet boundary to the expansion process lends a kind of self-adjustment to back-pressure variations.
- ...[they are] substantially shorter than comparable internal-flow nozzles.
- The main difficulties associated with these configurations arise in the process of adequately supporting and cooling the central plug.