There are a few edits you need to make to your js code.
(1) in your $(document).on('click', 'button.number', function () { you need to check if the current value is a .function (operator), and if so add the operator to memory before setting the value to the number. I used $.inArray($show.val(),['+','-','x','/']) !== -1 which checks to see if it is in the array.
(2) changing your $("#add").click(function () { to $(document).on('click', 'button.function', function () { allows you to use all your .function (operator) buttons for this code, and not just the +.
(3) you need to add the current value to memory before you post memory to your php.
(4) you need to change execute: $.show.val() to execute: memory 
$(function () {
var $show = $('#display');
var currentDisplay = "";
$show.val(0);
$(document).on('click', 'button.number', function () {
    if ($show.val().length >= 8) {
        $show.val("Error");
    } else if ($show.val() == "Error") {
        $show.val("0");
    } 
    // (1) check if current value is a .function
    else if ($.inArray($show.val(),['+','-','x','/']) !== -1) {       
        var addOp = $show.val();
        if (addOp) memory.push(addOp);
        $show.val($(this).val());
    } 
    else {
        $show.val(($show.val() == "0" ? "" : $show.val()) + $(this).val());
    }
});
$("#clear").click(function () {
    $show.val("0");
});
$("#ce").click(function () {
    if ($show.val().length >= 2) {
        $show.val($show.val().substring(0, $show.val().length - 1));
    } else {
        $("#ce").trigger("click");
    }
});
var memory = [];
// (2) changed from $("#add").click(function () { so all functions are registered
$(document).on('click', 'button.function', function () {
    var addnum = $show.val();
    if (addnum) memory.push(addnum);
    $show.val($(this).val());
});
$('#equ').click(function () {
    // (3) add current value to memory
    var addnum = $show.val();
    memory.push(addnum);
    // (4) change execute: $show.val() to execute: memory
    $.post("calculation.php", {
        execute: memory
    }, function (data,status) {
        $show.val(data);
        var e = memory.join('');
        memory = [];
    });
});
});
Then in calculation.php you want to loop through the array and add/subtract depending on the operator.
<?php
if(isset($_POST['execute']) && is_array($_POST['execute'])) {
    $total = (int)$_POST['execute'][0];
    for($i=1;$i<count($_POST['execute']);$i+=2){
        switch($_POST['execute'][$i]){
            case '+': $total += (int)$_POST['execute'][$i+1];break;
            case '-': $total -= (int)$_POST['execute'][$i+1];break;
            default : $total += (int)$_POST['execute'][$i+1];
        }
    }
    echo $total;
}
else echo 'Error';
?>
(note: I only did + and - in php, assuming that you could figure out how to add the * and /)
here is an updated jsFiddle - http://jsfiddle.net/9t78jd47/3/ (it uses js code, instead of $.post() to mimic sending memory to calculation.php