Problem-Trouble | Commonly Confused Words

Problem

/ˈprɒbləm/

A matter or issue that needs to be solved or dealt with

Finally Mr Micawber's problems reached a crisis.Say there's a problem.You must help me with my problem.

/ˈtrʌb(ə)l/

Difficulty or problems that cause distress or worry.

She troubled what to say, but finally observed:And then she began to tell me about all her troubles.Something is troubling him.

Problem is a more neutral, general term compared to trouble, which often implies difficulty or distress.
A problem usually has a solution or a logical approach to resolve it, while trouble can imply an ongoing problematic situation or emotional turmoil.
Problem can be used in mathematical or technical contexts, whereas trouble is more commonly associated with personal or emotional issues.