Only open one accordion tab at one time

To achieve this you need to reset the state of the accordion back to its original state on each click, before you set the required classes on the clicked elements. To do that you can extract functionality to set the class names in to their own function and call it as required. Try this:

var acc = document.getElementsByClassName("accordion");
var panel = document.getElementsByClassName('panel');

for (var i = 0; i < acc.length; i++) {
    acc[i].onclick = function() {
        var setClasses = !this.classList.contains('active');
        setClass(acc, 'active', 'remove');
        setClass(panel, 'show', 'remove');

        if (setClasses) {
            this.classList.toggle("active");
            this.nextElementSibling.classList.toggle("show");
        }
    }
}

function setClass(els, className, fnName) {
    for (var i = 0; i < els.length; i++) {
        els[i].classList[fnName](className);
    }
}

Working example

When selecting one item, you just need to hide all of them beforehand.

var acc = document.getElementsByClassName("accordion");
var i;

for (i = 0; i < acc.length; i++) {
    acc[i].onclick = function() {
        hideAll();

        this.classList.toggle("active");
        this.nextElementSibling.classList.toggle("show");
    }
}

function hideAll() {
    for (i = 0; i < acc.length; i++) {
        acc[i].classList.toggle("active", false);
        acc[i].nextElementSibling.classList.toggle("show", false);
    }
}

var acc = document.getElementsByClassName("accordion");
var i;
var last;
for (i = 0; i < acc.length; i++) {
    acc[i].onclick = function() {
        if(last){
            last.classList.toggle("active",false);
            last.nextElementSibling.classList.toggle("show",false);
        }
        this.classList.toggle("active");
        this.nextElementSibling.classList.toggle("show");
        last=this;
    }
}

variable last will track the last active accordion, so you don't need to iterate every accordion and panel again.