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
This error can also occur if you accidentally use commas instead of AND in the ON clause of a JOIN:
JOIN joined_table ON (joined_table.column = table.column, joined_table.column2 = table.column2)
^
should be AND, not a comma