What is the difference between a 1523e and 1523f?

One ends in "E" and the other ends in "F."

Software and firmware that's it

From the wiki: https://en.wikipedia.org/wiki/SINCGARS
The RT-1523E was designed to include all the features of the RT-1523C, at half the size and weight, with virtually no degradation in capabilities or performance relative to the SIP RT.
The RT-1523E introduced a new frequency hopping mode of operation, called SINCGARS Mode 2. The new SINCGARS Mode 2 comprises all the same Mode 1 FH configurations but under a new TRANSEC security umbrella. The RT-1523E is reprogrammable via the front panel data connector.

The RT-1523F pictured with SideHat provides a SINCGARS ASIP 2-channel radio, based upon the design of the RT-1523E. The RT-1523F program was structured into two phases. The first phase inserted the required physical and electrical interfaces into the ASIP RT-1523E in a manner that accommodates an Auxiliary Module, which provides the second channel. The second phase of the program developed the Auxiliary Module. The Auxiliary Module can be attached externally to the RT-1523F radio chassis on the left side when facing the front panel. The primary distinction between the RT-1523F and its predecessor RT-1523E is the addition of this interface.
The RT-1523F also introduced the Radio Based Combat ID (RBCI) capability. This enhancement allows the radio to operate as a RBCI Interrogator, a RBCI RE-Relay, and it allows it to add RBCI Responder functionality to any of its FH voice or data modes. The RT-1523F also introduced the Radio Based Situational Awareness (RBSA) enhancement to the existing SA capabilities of the ASIP radios.