Android EditText and Button on same line

Does it have to be Relative Layout?
I would suggest the following: set EditText layout_width to fill_parent and its layout_weight to 1, something like this:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_height="wrap_content" android:orientation="horizontal"
android:layout_width="fill_parent">
<EditText android:text="@+id/EditText01" 
    android:id="@+id/EditText01"
    android:layout_height="wrap_content" 
    android:layout_weight="1"
    android:layout_width="fill_parent">
</EditText>
<Button android:text="@+id/Button01" 
    android:id="@+id/Button01"
    android:layout_width="wrap_content" 
    android:layout_height="wrap_content">
</Button>

</LinearLayout>

In that case, the width for the EditText must be set to fill_parent (instead of wrap_content):

<RelativeLayout android:id="@+id/RelativeLayout01" android:layout_width="fill_parent" android:layout_height="wrap_content">
        <EditText android:id="@+id/search_box" 
            android:layout_alignParentLeft="true"
            android:layout_centerVertical="true"
            android:layout_width="fill_parent"
            android:layout_height="wrap_content"
            android:hint="type to filter"
            android:inputType="text"
            android:maxLines="1" />
        <Button android:id="@+id/search_text"
            android:layout_toRightOf="@id/search_box"
            android:text="Search"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"/>
  </RelativeLayout>

Edit

As you said, it hides the button. Then, just invert the order:

<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout
    android:id="@+id/RelativeLayout01" android:layout_width="fill_parent"
    android:layout_height="wrap_content">
        <Button android:id="@+id/search_text"
            android:layout_alignParentRight="true"
            android:text="Search"
            android:layout_width="wrap_content"
            android:layout_height="wrap_content"/>
        <EditText android:id="@+id/search_box" 
            android:layout_alignParentLeft="true"
            android:layout_toLeftOf="@id/search_text"
            android:layout_centerVertical="true"
            android:layout_width="fill_parent"
            android:layout_height="wrap_content"
            android:hint="type to filter"
            android:inputType="text"
            android:maxLines="1" />
</RelativeLayout>