Using EnumMemberAttribute and doing automatic string conversions

If your project references Newtonsoft.Json (what doesn't these days?!), then there is a simple one line solution that doesn't need reflection:

public static string ToEnumString<T>(T value)
{
   return JsonConvert.SerializeObject(value).Replace("\"", "");
}

public static T ToEnum<T>(string value)
{
   return JsonConvert.DeserializeObject<T>($"\"{value}\"");
}

The ToEnumString method will only work if you have the StringEnumConverter registered in your JsonSerializerSettings (see JavaScriptSerializer - JSON serialization of enum as string), e.g.

JsonConvert.DefaultSettings = () => new JsonSerializerSettings
{
    Converters = { new StringEnumConverter() }
};

Another advantage of this method is that if only some of your enum elements have the member attribute, things still work as expected, e.g.

public enum CarEnum
{
    Ford,
    Volkswagen,
    [EnumMember(Value = "Aston Martin")]
    AstonMartin
}

Here is my proposition - it should give you the idea on how to do this (check also Getting attributes of Enum's value):

public static string ToEnumString<T>(T type)
{
    var enumType = typeof (T);
    var name = Enum.GetName(enumType, type);
    var enumMemberAttribute = ((EnumMemberAttribute[])enumType.GetField(name).GetCustomAttributes(typeof(EnumMemberAttribute), true)).Single();
    return enumMemberAttribute.Value;
}

public static T ToEnum<T>(string str)
{
    var enumType = typeof(T);
    foreach (var name in Enum.GetNames(enumType))
    {
        var enumMemberAttribute = ((EnumMemberAttribute[])enumType.GetField(name).GetCustomAttributes(typeof(EnumMemberAttribute), true)).Single();
        if (enumMemberAttribute.Value == str) return (T)Enum.Parse(enumType, name);
    }
    //throw exception or whatever handling you want or
    return default(T);
}