Long processing time microservice

I am setting up a microservice from the ground up that several other services will make requests to. I am wondering what would be the best approach to handling the requests i.e. API, messaging or SSE. The issue I am going to face when implementing this service is the processing time will take a very long time (hours). I would ideally like to return a JSON, or objects in the case of messaging with the data produced by this service, but I worry about timing out API calls or messages. What would be the best/alternative approaches to take for this situation, or if sending a JSON/object is unreasonable here what might I do to get data to the requesting service?

Additional question about SSE, can I use that for server to server communication or is that strictly for browsers?

Cheers