Prueba esto:
Código PHP:
<html >
<head>
<title>Sumando</title>
</head>
<body>
<form name="form1" method="post" action="">
<p>
Numero 1:
<input onkeyup="if(form1.textfield2.value!=''){form1.textfield3.value = parseInt(this.value)+parseInt(form1.textfield2.value)}" name="textfield1" type="text" size="8" maxlength="8">
</p>
<p>
Numero 2:
<input onkeyup="if(form1.textfield2.value!=''){form1.textfield3.value = parseInt(this.value)+parseInt(form1.textfield1.value)}" name="textfield2" type="text" size="8" maxlength="8">
</p>
<p>Resultado es: <input name="textfield3" type="text" size="10" maxlength="10">
</p>
</form>
</body>
</html>