Poison reverse is an extra add-on to the split horizon rule that overrides split horizon in cases exactly like you describe. The route with the infinite metric is sent from A to B and E, and from B and E to their connected neighbors, including A. The whole point is to get the entire network into a converged understanding that T and any networks behind it are no longer reachable.
Here's a quote from the Wikipedia page for split horizon that took me less than 5 seconds to find with a Google search (still not getting the hint are we?):
Split-horizon routing with poison reverse is a variant of split-horizon route advertising in which a router actively advertises routes as unreachable over the interface over which they were learned by setting the route metric to infinite (16 for RIP). The effect of such an announcement is to immediately remove most looping routes before they can propagate through the network. The router is said to have poisoned the network by sending 'false' (infinite) metric values to other devices sharing such updates. The main disadvantage of poison reverse is that it can significantly increase the size of routing announcements in certain fairly common network topologies, but it allows for the improvement of the overall efficiency of the network in case of faults. Split horizon states that if a neighboring router sends a route to a router, the receiving router will not propagate this route back to the advertising router on the same interface. With route poisoning, when a router detects that one of its connected routes has failed, the router will poison the route by assigning an infinite metric to it and advertising it to neighbors. When a router advertises a poisoned route to its neighbors, its neighbors break the rule of split horizon and send back to the originator the same poisoned route, called a poison reverse. In order to give the router enough time to propagate the poisoned route and to ensure that no routing loops occur while propagation occurs, the routers implement a hold-down mechanism.