Automatically login to Wordpress from another web application

I have a site A which deploys and configures Wordpress instance for user Y (users are managed by site A). Together with the installation, it creates a Wordpress user X.

User Y (logged in) can click on a link on site A which opens the Wordpress instance in a new window. I do not want the user to login to the Wordpress instance separately, but rather somehow automatically log him in as user X (so it would be "hidden" for the user). Hence, the user opens Wordpress from site A and is automatically logged in.

I have access to both applications (site A and Wordpress instance) and can deploy any code to each.

How would you solve this? Which pattern would you go with?