[HttpClient][1] is what you're after.
To add headers, you simply create a custom HttpRequestMessage:
Dim client As New HttpClient()
Dim request As New HttpRequestMessage() With
{
.RequestUri = New Uri("http://staging-exact-integration.posios.com/PosServer/rest/core/company"),
.Method = HttpMethod.Get,
}
request.Headers.Add("X-Auth-Token", "eyJhbGciOiJIUzI1NiJ9.eyJleHAiOjE0NTc3NTQ1")
Dim result = client.SendAsync(request).Result
[1]: https://msdn.microsoft.com/en-us/library/system.net.http.httpclient%28v=vs.118%29.aspx