"Knowing that the maximum current that could flow into the LED is 36V/2kOhm = 18mA"
Yes, but that statement implies that at 18mA the whole 36V would be dropped over the resistor, and actual volatage over diode would be 0 (zero) volts. :) (I had to include this for newbies, that could be misguided by statement, even as it probably meant just that in no case current can go over 18mA.) For diode it does not matter what voltage you input to the whole circuit, all the diode feels is the voltage between its two legs.
Trouble is voltage drop over resistor is porportional to the current, so if diode blocks the current completly ... no voltage drop on the resistor, and the whole supply voltage lands on diode itself.
In reality actual voltages over diode and the resistor is the result of the equilibrium.
Diode might pass some current in reverse ... if it is not destroyed in shortcircuit mode (usualy it fails open to open circuit), so not so much voltage gets droped over resistor.
BUT. But it really depends on the diode characteristics (which you seldom find in spects for range above stated max reevesre voltage, and many times not at all as graph for revesrse voltage (only reverse current at max rev.V).
I have 5mm amber LED with Vf of about 2.2V which I tested and blocks current completly up to 41V (did not use higher voltage source) (voltage drop over 2K resistor was 0 mV).
Red 3mm LED with Vf about 2V, let some current in reverse even before 5V and wih higher voltage it got worse fast. But after putting LED back in "proper" way, it works as usual again.
Most currious is 3mm BLUE LED (rated 5mA, 3V) which gave enough light to be clearly visible in lighted surrounding conditions even at 50 micro amperes (yes, 0.05 mA) originaly. (Now after much missuse (bellow) things are different).
This LED lets even more current in reverse than it lets forward at the same voltage.
I reversebiased it to first to 22V and later to 40V for few secconds, where it let 18mA through (remember 5mA rated) in reverse!
When i forward biased it again it DID NOT LIGT. Dead?
No, after first abuse, it took near 16V of forward voltage to let any current through (I monitored voltage on 2K resistor, to detect current) an light it, as it light, forward voltage returned to near original value, and subsequently started at similar voltage as usual.
After second abuse (40V reverse) it took even higher voltage (over 20V) to start again forward biased, but Vf permanently dropped to about 2V, and now it takes about 2.5mA at Vd of 2.45V (Supply voltage to circuit 8.9V) to light it the same as it lighted at only 0.05 mA originally.
BTW, I noticed simmilar fast deterioration effect at some chaep red laser diodes run at only close to 20mA (it's rated current).
None of the tested diodes did light reverse biased (not even slightly), at any reverse current (even 3x rated current), and none was destroyed by high reverse bisas. Except last case blue diode, other exibited no harm I coould notice form high reversal.