You can't, but... If you own both pages then...
1) You can send the data via query params (http://siteB.com/?key=value)
2) You can create an iframe of Site B inside site A and you can send post messages from one place to the other. As Site B is the owner of site B cookies it will be able to set whatever value you need by processing the correct post message. (You should prevent other unwanted senders to send messages to you! that is up to you and the mechanism you decide to use to prevent that from happening)