Use the API to find a username based on an email?

In lieu of a bump, let me describe what I want to do.

On my CMS, I have a bunch of user profiles. On each profile I want to display that user’s activity on Discourse, which I would get via RSS.

For example, my activity on this Discourse is available here:
https://meta.discourse.org/users/alehandrof/activity.rss

To get this URL I need a username, but I don’t have this data at the CMS. All I have is users’ email, which is the same in both the CMS & Discourse. (I’ve made sure of this manually for now, since it’s a small community, but I will be implementing SSO in the near future.)

It’s a PHP CMS and I’ll write a small add-on that pings Discourse with the email and gets a username in return. I will then use the username to form the URL and give it to a plugin that will consume the RSS feed and allow me to output it with my own HTML.

Is there an API endpoint that allows me to find a user’s username through their email?