The correct answer is: E. No error
The sentence is grammatically correct. The word “unintentionally” is an adverb that modifies the verb “let.” The word “out” is a preposition that shows the direction of the action. The word “secret” is the direct object of the verb “let.” The word “by” is a preposition that introduces the phrase “talking about it loudly in the library.” The word “it” is a pronoun that refers to the secret. The word “loudly” is an adverb that
modifies the verb “talking.” The word “in the library” is a prepositional phrase that modifies the verb “talking.”The sentence is clear and concise. It conveys the intended meaning without any ambiguity. The sentence is also consistent with the rules of grammar.