The most common and most likely answer to this crossword clue is the 5 plus 3 plus 4 letter word LANCE THE BOIL
I've seen this crossword clue in Financial Times
L
A
N
C
E
T
H
E
B
O
I
L
Buddy explains!
The straight part
We know that "Deal with problem" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deal with problem = lance the boil.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.