What is wrong about this interpretation of QFE and QNH?
Your question is quite not clear, you are challenging definitions and use of definitions, but you may start with a misunderstanding:


  QFE = pressure measured by an altimeter which is adjusted to ground
  level (it gives a height of 0 when the airplane is on the ground).




Definitions

To ensure clarity, QFE/QNH:


are reference pressures, not altitudes
are not read/measured by the altimeter, but entered by the pilot in the setting window.
when mentioned in an altitude would be mentioned like, for instance: "I'm flying at 1,000 ft referenced to QFE", and not "my QFE is 1,000 ft".


QFE and QNH are not what the needles of the altimeter indicate, they are only the pressures that are to be entered in the setting window to calibrate the altimeter for common low level flight references.



How is QNH determined

While QFE is a direct measurement of the pressure, where the temperature is ignored, QNH is never measured, it is "retro-computed" from QFE:


Determining QNH requires first to know the local pressure (QFE) at the relevant location (e.g. airfield reference point)
The actual altitude of this location is then converted into a pressure difference, using the ISA model (+1 hPa per 27 ft at low altitude), without taking into consideration the temperature
The offset (which is positive unless the airfield altitude is under sea level) is added to QFE, the result is QNH (hence QNH pressure is usually > QFE pressure)


Said otherwise: QNH is the theoretical pressure value at MSL. but as the temperature wasn't taken into account, and actual distance between isobaric surfaces vary with actual temperature, then the actual pressure at MSL (if it could be measured) would be likely different.



Altimeter readings

After calibration with QFE or QNH value, any change in actual pressure -- that can be due to an actual altitude change, a local temperature change or a local pressure change -- will be sensed by the altimeter, the pressure change being indicated by an altitude change at the ISA rate of -27 ft for each added hPa.

By principle when the altimeter is on an isobaric surface equal to any pressure entered in the window, the value read is zero. As by definition the QFE is the pressure at the airfield level, then if the altimeter is at the airfield, set to QFE, and QFE has been just updated, then it indicates 0 altitude above ground level (AGL).

More generally (I hope this is accurate, else correct me):

  

Note that the pressure scale on the left has the higher value at the bottom, while the altitude scale on the right has it at the top.


  As you can see this figure says that $h_{QFE}=h_{QNH}+h_e$ which should 
  instead be $h_{QNH}=h_{QFE}+h_e$ (the opposite).


You or the book may be correct, depending on the sign of $h_e$. But it's not clear. If this quantity is positive, you are correct.

Remember that QFE and QNH are not altitudes, they are the altimeter reference values. For an airfield above MSL, QFE &lt; QNH and an altimeter reading (h) referenced to QFE ($h_{QFE}$) will be approximately the height above the airfied (AGL) while when referenced to QNH ($h_{QNH}$) it will be approximately the altitude above MSL (AMSL).

Indeed altitude above sea level is larger than height above ground. Possibly in your example above, the author may have $h_e$ as a negative value.