Since pressure changes with elevation, in order to compare relative high and low air pressure areas, they all must account for this elevation-related pressure change. Otherwise, there would be a permanent low pressure area over all the mountains (where the measuring station is at relatively high elevation) and a permanent high pressure in all the valleys (where the measuring station is at relatively low elevation) and no relative comparisons would be able to be made.

The way this is accounted for is by "reducing" all measured atmospheric pressure readings down to sea level. This way, since all pressure readings will be based on the SAME altitude(ie. sea level), all altitude related pressure anomalies will be removed and a pure air mass pressure comparison can be made. This how high and low pressure air masses are identified and quantified.

The way this is accomplished is by using an average assumed atmospheric pressure change for a given altitude. This assumed value (which is the same assumption aviation altimeters work with) is that pressure will decrease 1 inch of Hg for every 1,000ft of altitude above sea level.

An example is on a standard (29.92) day, the actual measured pressure at Denver (assuming 5,000 ft elevation) would be 24.92 because, assuming 1 Hg / 1,000ft pressure decrease, the pressure would be 5 inches of Hg lower than what it would be at sea level due to the 5,000ft elevation above sea level.

So, when you read an altimeter setting in Denver, you are actually reading the measured pressure at Denver REDUCED (using the 1 Hg/1,000ft assumption) to sea level (zero altitude). This reduction done to altimeter settings is what allows us to always know our height above SEA LEVEL (not just the local area elevation).

In the OP' original question, QNH is the altimeter setting reduced to sea level and the QFE is the ACTUAL measured pressure at the field (no sea level reducion = includes altitude-related pressure decreases).

So, on a standard day in Denver (5,000 ft field elevation:

QNH = 29.92 Hg (reduced to sea level)
- Altimeter would read 5,000 ft when set to QNH = Altimeter would read altitude above sea level

QFE = 24.92 Hg (NOT reduced to sea level = ambient pressure)
- Altimeter would read zero ft when set to QFE = Altimeter would read altitude above ground level