There is a rule in writing called "show don't tell." However, I noticed some writers such as George R. R. Martin and J. K. Rowling occasionally break this rule. Are there exceptions to this rule?

Yes, the exceptions would be any situation in which telling is better.

There are few ‘rules’ more pernicious than this one. It’s so snappy, it’s so absolute. DON’T tell. Well, my rule would be, mistrust any writing advice snappy enough to go on a T-shirt.

I understand what the rule aims at. The idea is that it’s more vivid to describe someone being angry than just telling us that they’re angry. If we just told all the time, the book would resemble a summary of a book rather than an actual story. Equally, if we just show all the time, the book would be a thousand pages long, and involve paragraphs of description every time we wanted to convey anything.

I can certainly think of situations and contexts where telling is better than showing, depending on what you’re trying to do. I opened a book at random and read ‘Del was a tall man, knobbly, ungainly’. We might object to ‘ungainly’ on the basis that we ought to show Del being ungainly; but we won’t have a chance for a while in this scene as he’s sitting in a bar, talking, for most of it; and if he is somehow awkward or clumsy, we’d have to invent some business for him in order to sell it. It’s not necessary; his ungainliness is just part of that thumbnail sketch, and if it is indeed telling, it’s fine.

It’s possible to take this too far. You can imagine red-penciling ‘It was the best of times, it was the worst of times’, or ‘It is a truth universally acknowledged…’ etc.