Well, as best as I remember (some time ago, from Chemistry courses, so I may be mis-remembering), it goes something like this.

The Schroedinger wave equation assigns to some quantum entity (a "particle"), roughly speaking, its energy, given by the frequency of the wave. Schroedinger's equation, of course, resolves to a sine function, a "sine wave"

It was Mach (I think) who pointed out that the square of this function should be interpreted as the probability density for the particle's location. Let's go with that.

Now, if the square of Schroedinger's psi function is a probability density for location, it follows that, knowing the exact energy of a particle implies a mere probability for its location.

Suppose now we know our particle's exact location. This is best described by a psi-squared wave that is zero almost everywhere, i.e. a flat line with a single peak = location with probability = 1. But the only way to generate such a curve is by "mixing together" (it's called superposition) of all possible energy waves for our particle in such a way that they destructively interfere at all but one point, the location.

But, as we needed the superposition of all allowable energies to find the exact location, and that knowing the exact energy merely gives us a probability for location, it follows that we cannot simultaneously know both, to any degree of accuracy.

Note that this has nothing to do with the precision of measuring instruments, nor photons hitting measurables, it is a matter of principle