Order by certain enum values first

I’ve got a table like:

╔═══╦════════════════════╦═════════════╗
║ID ║ type (enum)        ║ updated_at  ║
╠═══╬════════════════════╬═════════════╣
║ 1 ║ friend_request     ║ <date_time> ║
║ 2 ║ new_article        ║ <date_time> ║
║ 3 ║ article_read       ║ <date_time> ║
║ 4 ║ article_invitation ║ <date_time> ║
╚═══╩════════════════════╩═════════════╝

I would like to order the retrieved results by the value of the enum type.

Records with value friend_request and article_invitation for the type column should come first, then the rest. Everything together should be ordered by updated_at DESC.

Now, I know I can chain multiple order by properties, so f.e.

order by type desc, updated_at desc

will order for me by type and the result of that by the updated_at values. But how do I specify for certain values of the type column? Is that even possible?

order by case "type"
            when 'article_invitation' then 1
            when 'new_article' then 2
            when 'article_read' then 3
            when 'friend_request' then 4
         end, 
         updated_at desc