MySQL – Operand should contain 1 column(s)

Your subquery is selecting two columns, while you are using it to project one column (as part of the outer SELECT clause). You can only select one column from such a query in this context.

Consider joining to the users table instead; this will give you more flexibility when selecting what columns you want from users.

SELECT
topics.id,
topics.name,
topics.post_count,
topics.view_count,
COUNT( posts.solved_post ) AS solved_post,
users.username AS posted_by,
users.id AS posted_by_id

FROM topics

LEFT OUTER JOIN posts ON posts.topic_id = topics.id
LEFT OUTER JOIN users ON users.id = posts.posted_by

WHERE topics.cat_id = :cat
GROUP BY topics.id