die Lösung
solution
The answer to a question, riddle, or task.
Ich kenne die Lösung für dieses Kreuzworträtsel nicht.
I don't know the solution to this crossword puzzle.

solution
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solution
The answer to a question, riddle, or task.
Ich kenne die Lösung für dieses Kreuzworträtsel nicht.
I don't know the solution to this crossword puzzle.

'Die Lösung' (solution) is a noun derived from the verb 'lösen' (to solve). The ending '-ung' is a typical way in German to form feminine nouns from verbs that describe the process or result of the action.
Er versucht, das Rätsel zu lösen.
He is trying to solve the riddle.
When referring to a problem, 'Lösung' (solution) is very often used with the preposition 'für' (for). Typical verbs are 'eine Lösung finden' (to find a solution), 'eine Lösung suchen' (to look for a solution), or 'an einer Lösung arbeiten' (to work on a solution).
Wir müssen dringend eine Lösung für das Müllproblem finden.
We urgently need to find a solution to the waste problem.
You can recognize the chemical meaning from words in the field of science or cooking. The type of solution is often described more precisely, e.g. 'Salzlösung' (saline solution) or 'Zuckerlösung' (sugar solution).
Geben Sie das Salz in warmes Wasser, bis eine klare Lösung entsteht.
Add the salt to warm water until a clear solution forms.
This meaning is mainly used in formal or legal language when dealing with contracts or formal ties. The combinations 'die Lösung des Vertrags' (the termination of the contract) or 'die Lösung des Arbeitsverhältnisses' (the termination of the employment relationship) are typical.
Die Lösung des Vertrags ist nur unter bestimmten Bedingungen möglich.
The termination of the contract is only possible under certain conditions.
problem
'das Problem' and 'die Lösung' are often direct opposites. A problem is a difficulty, an open question, or a stressful situation. A solution is the answer or the way to end that difficulty or deal with it better. So you first talk about the problem and then look for a solution. This contrast fits very well with tasks, technology, work, or personal difficulties.

Nach dem Gespräch findet das Team endlich eine Lösung.
After the discussion, the team finally finds a solution.
Im Büro gibt es ein Problem mit dem neuen Drucker.
There is a problem with the new printer at the office.