I found a solution that worked.
I placed the follwing Javascript on the popup page:
function button_click()
{
window.opener.addHTML(document.Form1.customHTML.value);
}
Then I placed this Javascript on my CE page:
function addHTML(html)
{
var editor1 = document.getElementById('<%=Editor1.ClientID%>');
editor1.PasteHTML(html);
}