Take on a problem in southeast (6)
I believe the answer is:
assume
'take on' is the definition.
(I know that take on can be written as assume)
'a problem in southeast' is the wordplay.
'problem' becomes 'sum' (arithmetic problem).
'in' is an insertion indicator.
'southeast' becomes 'SE' (synonyms).
'sum' placed within 'se' is 'ssume'.
'a'+'ssume'='ASSUME'
(Other definitions for assume that I've seen before include "Take (control)" , "Believe" , "Tale of the gods" , "Take as true or take for granted" , "Dark brown fur" .)