<span class="datetimepicker-span" @onclick="@OnOpenHandler">
    <TelerikDateTimePicker Class="my-date-time-picker" Value="@selectedTime"
                           Format="dd MMM yyyy HH:mm:ss" Width="250px"></TelerikDateTimePicker>
</span>

@code {
    public DateTime? selectedTime { get; set; }

    public bool isOpened { get; set; } = false;

    public void  OnOpenHandler()
    {
        isOpened = !isOpened;

        if (isOpened)
        {
            Console.WriteLine("DateTimePicker was opened.");
        }
        else
        {
            Console.WriteLine("DateTimePicker was closed.");
        }
    }
}