You can usually understand these things by writing a temporary macro, doing what you want to do, and see what happened in the macro editor.
In fact, this is a case where it is probably only by recording a temporary macro that you can figure out how to do it. Here is the solution explorer update command:
DTE.Commands.Raise("{1496A755-94DE-11D0-8C3F-00C04FC2AAE2}", 222, null, null)
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