Cryptic crossword clue
Period yielding 10 addled brain? Of course! 13

The most common and most likely answer to this crossword clue is the 13 letter word CARBONIFEROUS

I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Period yielding 10" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case period yielding 10 = carboniferous.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does CARBONIFEROUS mean?

CARBONIFEROUS adjective
  1. Containing or producing carbon.

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