This actually pretty simple. Use a free command line tool called cURL to open an incident using the ServiceNow API. You will need an account that has the rest_service role in your ServiceNow instance.
Install cURL on your Solarwinds server. In Alert Manager, create a trigger action to "execute an external application" (which is cURL)
Example: (note that I had to escape the quotations because it's running on Windows)
c:\pathto\curl.exe -X POST -H "Accept: application/json" -H "Authorization: Basic your-encoded-auth-hash" -H "Content-Type: application/json" -d "{\"short_description\":'${NodeName} is ${Status}!!!!',\"comments\":'${NodeDetailsURL}',\"opened_by\":\"Solarwinds\",\"assignment_group\":\"network\",\"impact\":\"1\",\"urgency\":\"1\"}" https://yourinstance.service-now.com/api/now/v1/table/incident"
Use this wiki site for REST reference http://wiki.servicenow.com/index.php?title=Getting_Started_with_REST