If the LEDs are desoldered, then the legs are cut... so there is no leg that is longer than the other.
![Sad :(](https://cdn.geekhack.org/Smileys/solosmileys/sad.gif)
"Reversing the polarity" may sound like something out of Star Trek, but it is as simple as to swap + and - .
If the LEDs are somewhat transparent then you will be able to see the innards if you have good eye sight. Those innards are often a bit asymmetric and once you have figured out which legs are + and - on one LED in the pile then you should be able to find the polarity on the others as well.
Or you could build a LED tester. Connect a 3V battery pack, a resistor and two empty terminals in series. Then test the LED against those terminals to figure out which direction works. The resistor is necessary to not burn the LED.
I dunno about the value of the resistor though ... You could check a web site that sells LEDs what the LEDs are rated at, then google for a "LED Resistor calculator".