This is sort of an anomalous stat since normally new visits should be lesser or equal to unique visitors for that period. However, you are making a mistake in your interpretation, so let's break it down. The data basically says this:
- 10 unique visitors:
- There were 10 hits (in this period) to your site where GA found no prior hits (in this period) for that visitor.
- So that means there was a total of 10 different users that visited your site in this period.
- 26 visits (11 new + 15 return):
- There were 26 different GA-identified browser sessions (in this period).
- 11 sessions were by users whom GA had never seen before.
- 15 sessions were by users whom GA has seen before.
Before we get to your edge case, let's address a more common case, where there are 10 new visits + 15 returning visits, but only 10 unique visitors:
Now, you might say, shouldn't there be at least 11 unique visitors since each new visit = 1 unique visitor, and all return visits together require at least another unique visitor? Well, no. A unique visitor can, in this case, contribute 0 or 1 new/first visits and an arbitrary number of return/subsequent visits. So at minimum, you'd only need as many unique visitors as you have new visits.
But wait, how on earth did you end up with 1 more new visit than unique visitors? That should be impossible!
So how does this explain what's going on here? One possibility is that there was at least 1 user who had cookies disabled, and they had at least 1 session, creating a visit that couldn't be matched with a previous session, thus creating a new visit. And since cookies were disabled, they didn't register a new unique visitor.