The answer to your question would be that the verbs that correctly complete the sentence are the following one: Were and Are. Therefore, the sentence would be as follows: Solar flares were the cause of the difficulty, and new instruments are the solution.
The subjects of the two clauses are plural noun phrases, so the verbs must also be plural for subjects and predicates to agree in number. Subject verb agreement means that the subject and the verb must agree in number. This means both need to be singular or both need to be plural.