The official Tumblr app has been withdrawn from the Windows Store and cannot be used anymore. Users who are still using the platform can use the service by heading over to the official website. When asked by a fan about the status of the Tumblr app, a company rep responded in an email stating that they are no longer supporting the Windows Phone version.
https://twitter.com/sabriyurga/status/702258894098321408
There is no information if there are any plans to release a Windows 10 version of the app.