No not really. You have 2 backups.
The older one which I am assuming contains the bulk of your posts until a week ago?
A newer one which will only contain the last 7 days posts?
Whichever one you import back into your database, will be the one that is in place.
So, I would:
1. Manually copy the past 7 days post to a text files [with comments info]
2. Restore old backup
3. Copy/paste the last 7 days back into new posts [time stamped if necessary]
4. Make a new backup
The other option is to wait until some much more intelligent soul than me tells you how to add the posts/comments from the past 7 days via a database query.