Trying to write this query that self joins using the query builder

I'm trying to write:

SELECT a.id FROM posts a INNER JOIN ( SELECT DATE(timestamp) date, MAX(likes) max_likes FROM posts GROUP BY DATE(timestamp)) b ON DATE(a.timestamp) = b.date AND a.likes = b.max_likes

The inner join is simple, it's:

$inner = DB::table('posts as b')
                   ->selectRaw('date(timestamp) date')
                   ->groupBy(DB::raw('date(timestamp)'));

I'm just not sure how to get started on the outer...

$outer = DB::table('posts as a')
               ->selectRaw('a.id')
               ->join($inner)
               ->whereRaw(['DATE(a.timestamp) = b.date'], ['a.likes = b.max_likes']);