Could you please explain what you mean by the "left" and "right" sides of a resistor. It would be most helpful if you could post a diagram showing what you mean. Resistors are not always mounted horizontally, nor are they always drawn horizontally on diagrams, so it is better not to refer to "left" and "right" except in relation to a drawing.
However, it seems likely that "left" and "right" refer to the terminations of the resistor, and that the voltages are measured from each "side" to a common point such as ground. In this case it does follow from Kirchhoff's Voltage Law that the voltage across the resistor is given by subtracting the terminal voltages measured to a common point.
This method can be useful when one terminal of a measuring instrument cannot be connected to high potential, but any value found by subtracting two measurements is likely to be less accurate than a direct measurement - especially where the measurements have the same sign and similar values.
This may be complicated by voltage drops caused by the current drawn by measuring instruments. There may be further errors if the voltages are varying and the two measurements are not obtained at the same time.
The bottom line is that in theory knowing two of the voltages defines the third, but that some limitations apply to using this result to make practical measurements.
