With a bit of ES6 magic it can be fairly concise. Note that we need to check both ways around in case there are unique items in either array.
const arr1 = [1, 2, 3, 4, 5];
const arr2 = [1, 3, 8];
let unique1 = arr1.filter((o) => arr2.indexOf(o) === -1);
let unique2 = arr2.filter((o) => arr1.indexOf(o) === -1);
const unique = unique1.concat(unique2);
console.log(unique);
// >> [2, 4, 5, 8]