It depends on what train you take.

It looks like...
The InterCity/EuroCity trains cost 10€.
The ICE (high-speed) trains cost 16€
These trains take approx. 21-26 minutes from Hauptbahnhof to Hauptbahnhof, and these fares are Deutsche Bahn fares.

The regional trains (e.g., RE) trains are part of the regional transit network fares; those trains take just over 30 minutes to go from Düsseldorf to Cologne, if they are running on schedule. As I said, Düsseldorf and Köln are in different networks, but they do work together and have a fare structure called the RegioTicket. For Düsseldorf-Köln, you'd need 5Ü, which is 9,30€ for a single ticket and 31,50€ for a 4-trip ticket. A weekly ticket would be 48,20€ (valid Monday-Sunday). A day ticket for one person is 19€ and for up to five people traveling together, 23€.

There's also the SchönerTagTicket NRW, which is a day pass for all of the local transit in North Rhine Westphalia: 22€ for one person and 29,50€ for up to five people.

Now that I've thrown out too many numbers, I thought of something better.
Since your trade fair pass includes VRR travel, I think you'd just need an AnschlussTicket (extension ticket) to cover the trip from the tariff border to Cologne (Langenfeld-Köln, most likely). I don't know the exact price, but it should be about 5€ each way.

Probably too much info. There's a confusing array of tariffs and ticket options.