I am trying to join the Exchange Server 2013 (Server 2012 Standard) on to Sever 2012 Essentials via the Set up Exchange Server Integration wizard.

The wizard keeps failing:

There was a problem configuring the Integration
An unknown error occurred.
Make sure that the computer is connected to the network, and then try again.
If you continue to experience this problem, restart the server and then try again.

Both Servers are connected to the same domain via AD. I can see both Servers on the network and gain access to each server.

I have noticed that the Exchange server does not show up in the Dashboard under Devices. I cant seem to find a way of connecting the Exchange Server to Server 2012 Essen

Thats what I thought, but when I ran it I just get:

This computer is running a version of the Windows operating system that is not supported on connect to the server.

I am running Server 2012 Standard.

That is how both of the servers are connected, but I'm not going to be able to create an exchange account through Essentials as I would if they were both connected as they should be.

So let's confirm - you've either used the connect process to join the member server or manually joined it to the domain so it's listed as a member server in ADUC.  You've installed Exchange on the member server.   Now you've run the wizard in the console that runs a routine that ensures that when you add a user in the Essentials console it also adds a mailbox in the Exchange server.

When you say  it does not give you the ability to fully manage user accounts can you be specific about what is not happening?

Can you share the SharedServicesHost-EmailProviderServiceConfig.log this file should be on the server in the folder C:\ProgramData\Microsoft\Windows Server\Logs

We should have some errors or exceptions in this file. Look for lines which contain "PSRunspace"