Binding and DependencyProperty

<ResourceDictionary
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:ValidationTest"
    xmlns:controls="using:ValidationTest.Controls">

    <Style TargetType="controls:ValidationTextBox">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="controls:ValidationTextBox">
                    <Grid ColumnSpacing="12">
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition Width="*" />
                            <ColumnDefinition Width="Auto" />
                        </Grid.ColumnDefinitions>

                        <TextBox x:Name="TextBox" Grid.Column="0" Header="Test" Text="{TemplateBinding Text}" Description="Test" PlaceholderText="Test" />
                        <FontIcon x:Name="ErrorIcon" Grid.Column="1" Glyph="&#xE814;" Foreground="Orange" Visibility="Visible" />
                    </Grid>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>
</ResourceDictionary>

<ResourceDictionary
    xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
    xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
    xmlns:local="using:ValidationTest"
    xmlns:controls="using:ValidationTest.Controls">

    <Style TargetType="controls:ValidationTextBox">
        <Setter Property="Template">
            <Setter.Value>
                <ControlTemplate TargetType="controls:ValidationTextBox">
                    <Grid ColumnSpacing="12">
                        <Grid.ColumnDefinitions>
                            <ColumnDefinition Width="*" />
                            <ColumnDefinition Width="Auto" />
                        </Grid.ColumnDefinitions>

                        <TextBox x:Name="TextBox" Grid.Column="0" Header="Test" Text="{TemplateBinding Text}" Description="Test" PlaceholderText="Test" />
                        <FontIcon x:Name="ErrorIcon" Grid.Column="1" Glyph="&#xE814;" Foreground="Orange" Visibility="Visible" />
                    </Grid>
                </ControlTemplate>
            </Setter.Value>
        </Setter>
    </Style>
</ResourceDictionary>

public sealed class ValidationTextBox : Control
{
    public ValidationTextBox()
    {
        this.DefaultStyleKey = typeof(ValidationTextBox);
    }

    public string Text
    {
        get => (string)GetValue(TextProperty);
        set => SetValue(TextProperty, value);
    }

    public static readonly DependencyProperty TextProperty = DependencyProperty.Register(nameof(Text), typeof(string), typeof(ValidationTextBox), new PropertyMetadata(default(string)));
}

public sealed class ValidationTextBox : Control
{
    public ValidationTextBox()
    {
        this.DefaultStyleKey = typeof(ValidationTextBox);
    }

    public string Text
    {
        get => (string)GetValue(TextProperty);
        set => SetValue(TextProperty, value);
    }

    public static readonly DependencyProperty TextProperty = DependencyProperty.Register(nameof(Text), typeof(string), typeof(ValidationTextBox), new PropertyMetadata(default(string)));
}