You split the string by "End:", then work on individual string of the array. Something like this:
Code:
Dim s As String = "Start: 10/8/2008 End: 10/14/2008"
Dim parts() As String = s.Split("End:")
Dim startDate As Date = Date.Parse(parts(0).Replace("Start:", "").Trim())
Dim endDate As Date = Date.Parse(parts(1).Trim())
And of course, you need to implement errror handling to your code, like using Date.TryParse instead of Date.Parse.
Since you know the format of the date, you can also use Date.TryParseExact and pass in the date format.