@Jack Yes. Of course. So if you place a resistor in series with the diode or if you take into account the internal bulk resistance of the diode, which the above equation does not do, then the result becomes more complex. In that case, you need to solve a different equation for \$I_\text{D}\$, which will require the use of the LambertW (branch 0.) This gets into some math. But technically KVL still applies. It's just that the math has gone "non-linear" on you.
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