Think of QNE this way . . . . "Normal En route"
eckhard: ...common usage accepts QNE as the ISA Standard Pressure setting of 1013.2 hPa, or 29.92 inches, always set above T/A.
Another definition of QNE that you are referring to is the 'altitude displayed on the altimeter at touchdown with 1013 set on the altimeter sub-scale'. It is also known as the "landing altimeter setting."
Within the latter meaning, the term would be of use when an extremely low QNH is outside an aircraft's altimeter sub-scale range, and the pilot requests aerodrome QNE from air traffic services. But such extreme atmospheric conditions occur primarily near the core of a tropical depression/cyclone/typhoon; where airplanes wouldn't be operating.
QNE can be calculated by deducting the QNH from 1013, multiplying the result by 27 (the appropriate pressure lapse rate per hPa) and adding the airfield elevation.
For example: QNH 960 hPa, airfield elevation 500 feet, pressure setting 1013.
QNE = 1013 –960 = 53 × 27 = 1431 + 500 = 1931 feet (the reading at touchdown).