Here are the two areas you need to cover: Networking and Solarwinds administration.
Networking: A good way to learn would be to enroll yourself in a networking class such as CompTIA Network+ and Cisco CCNA.
Getting certified in each will increase your knowledge and will help your career. Building your own home lab would be a great way to learn as well.
Solarwinds administration: A great (and cheapest) way to learn is to get hands-on experience with a live system running Solarwinds.
You may be able to do this using a test system at your work. Or you could have your system to use outside of work and install and run Solarwinds (sandbox).
You should also view all of the Solarwinds training videos (there are many) which will be a big help and the documentation (manuals, guides, etc.) too.
gcastoldi is right with those two options. Those are very good starting points.
As far as education goes, you can also look at your local community college or trade school for a Cisco Academy. The Cisco Academy is a good place to start and get your feet wet. You might even be able to get College credit for some of the courses. One thing I have learned over the years, is that when you want to study for a certification exam, the best thing to do is get yourself a goal. I find that as soon as I open the book I give myself 60 days to take the test. Any more than 60 days and I will begin to forget what I learned in the beginning.
Also think about going to school for your Bachelors degree. It will help when it comes time to find the next job.