You can use messaging for that. Fuse ESB comes with ActiveMQ as the messaging solution out of the box. Then you can have application A send a message to a queue, which application B pickup, and send back a response on a response queue, for application A to receive.
You can also use other kind of transports such as HTTP, web service, TCP, and many many more.
Fuse ESB comes also out of the box with Apache Camel which has a lot of transports and components ready to use. See the list here: http://camel.apache.org/components
I suggest you read the Fuse ESB production introduction guide at: https://access.redhat.com/knowledge/docs/en-US/Fuse_ESB_Enterprise/7.1/html-single/Product_Introduction/index.html