。
There's no need to suffer in silence.
Literal
Be-silent-[and-て] is-worrying [thing-こと] [topic-は] does-not-exist [emphatic-よ].
~ことはない is the standard frame for 'there is no need to X / no reason to X' — literally '(such) a thing as X-ing does not exist.' The full ~黙って悩んでいる ('worrying in silence') is nominalized by こと, then negated. A reassuring or advisory tone — the speaker is telling someone they don't have to bear something alone.