OriginalGriff has a nice solution, but if the timezone is not (UTC), it will not parse. I would instead remove that part before parsing:
string inp = "Mon, 18 Jun 2018 10:26:11 +0000 (UTC)";
inp = inp.Substring(0, inp.IndexOf(" ("));
string format = "ddd, d MMM yyyy hh:mm:ss zzzz";
DateTime dt;
if (!DateTime.TryParseExact(inp, format, CultureInfo.InvariantCulture, DateTimeStyles.None, out dt)) {
Console.WriteLine("Nope!");
}