Jimmy Kimmel and Stephen Colbert dropped by each other's late shows Tuesday at the Brooklyn Academy of Music for a crossover episode ... and shed some light on the high-stakes drama both programs have been through.

Obviously, Kimmel had the most to get off his chest ... finally spilling on just what happened when the 'Live' host learned ABC was pulling his show off the air "indefinitely" after his comments about Charlie Kirk's alleged killer created a firestorm.

As you know ... JK's show has since resumed ... but as you can see in the video, Kimmel tells Colbert when he first learned of the suspension, he thought the program was toast. Of course, he added some levity to the moment, and said he took the call in the bathroom.

In turn, Colbert talked about the moment CBS brass informed him the 'Late Show' would come to an end in May 2026 over purported financial decisions ... although some believe politics played a part since -- like Jimmy -- SC has been a vocal critic of President Trump.

Colbert told Kimmel as much as it hurts ... he's accepted the decision and is grateful for the iconic experience of filling David Letterman's shoes.

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And speaking of Trump ... prior to taping the crossover, Kimmel and Colbert snapped a picture on stage with fellow late-night host -- and Trump critic -- Seth Meyers ... that they all shared with the caption ... “Hi Donald!”