function getSelectionCharacterOffsetWithin(element) {
    var start = 0;
    var end = 0;
    var doc = element.ownerDocument || element.document;
    var win = doc.defaultView || doc.parentWindow;
    var sel;
    if (typeof win.getSelection != "undefined") {
        sel = win.getSelection();
        if (sel.rangeCount > 0) {
            var range = win.getSelection().getRangeAt(0);
            var preCaretRange = range.cloneRange();
            preCaretRange.selectNodeContents(element);
            preCaretRange.setEnd(range.startContainer, range.startOffset);
            start = preCaretRange.toString().length;
            preCaretRange.setEnd(range.endContainer, range.endOffset);
            end = preCaretRange.toString().length;
        }
    } else if ( (sel = doc.selection) && sel.type != "Control") {
        var textRange = sel.createRange();
        var preCaretTextRange = doc.body.createTextRange();
        preCaretTextRange.moveToElementText(element);
        preCaretTextRange.setEndPoint("EndToStart", textRange);
        start = preCaretTextRange.text.length;
        preCaretTextRange.setEndPoint("EndToEnd", textRange);
        end = preCaretTextRange.text.length;
    }
    return { start: start, end: end };
}

function reportSelection() {
  var selOffsets = getSelectionCharacterOffsetWithin( document.getElementById("editor") );
  document.getElementById("selectionLog").innerHTML = "Selection offsets: " + selOffsets.start + ", " + selOffsets.end;
}

window.onload = function() {
  document.addEventListener("selectionchange", reportSelection, false);
  document.addEventListener("mouseup", reportSelection, false);
  document.addEventListener("mousedown", reportSelection, false);
  document.addEventListener("keyup", reportSelection, false);
};

#editor {
  padding: 5px;
  border: solid green 1px;
}

Select something in the content below:

<div id="editor" contenteditable="true">A <i>wombat</i> is a marsupial native to <b>Australia</b></div>
<div id="selectionLog"></div>

var editor = null;
var output = null;

const getTextSelection = function (editor) {
    const selection = window.getSelection();

    if (selection != null && selection.rangeCount > 0) {
        const range = selection.getRangeAt(0);

        return {
            start: getTextLength(editor, range.startContainer, range.startOffset),
            end: getTextLength(editor, range.endContainer, range.endOffset)
        };
    } else
        return null;
}

const getTextLength = function (parent, node, offset) {
    var textLength = 0;

    if (node.nodeName == '#text')
        textLength += offset;
    else for (var i = 0; i < offset; i++)
        textLength += getNodeTextLength(node.childNodes[i]);

    if (node != parent)
        textLength += getTextLength(parent, node.parentNode, getNodeOffset(node));

    return textLength;
}

const getNodeTextLength = function (node) {
    var textLength = 0;

    if (node.nodeName == 'BR')
        textLength = 1;
    else if (node.nodeName == '#text')
        textLength = node.nodeValue.length;
    else if (node.childNodes != null)
        for (var i = 0; i < node.childNodes.length; i++)
            textLength += getNodeTextLength(node.childNodes[i]);

    return textLength;
}

const getNodeOffset = function (node) {
    return node == null ? -1 : 1 + getNodeOffset(node.previousSibling);
}

window.onload = function () {
    editor = document.querySelector('.editor');
    output = document.querySelector('#output');

    document.addEventListener('selectionchange', handleSelectionChange);
}

const handleSelectionChange = function () {
    if (isEditor(document.activeElement)) {
        const textSelection = getTextSelection(document.activeElement);

        if (textSelection != null) {
            const text = document.activeElement.innerText;
            const selection = text.slice(textSelection.start, textSelection.end);
            print(`Selection: [${selection}] (Start: ${textSelection.start}, End: ${textSelection.end})`);
        } else
            print('Selection is null!');
    } else
        print('Select some text above');
}

const isEditor = function (element) {
    return element != null && element.classList.contains('editor');
}

const print = function (message) {
    if (output != null)
        output.innerText = message;
    else
        console.log('output is null!');
}

* {
    font-family: 'Georgia', sans-serif;
    padding: 0;
    margin: 0;
}

body {
    margin: 16px;
}

.p {
    font-size: 16px;
    line-height: 24px;
    padding: 0 2px;
}

.editor {
    border: 1px solid #0000001e;
    border-radius: 2px;
    white-space: pre-wrap;
}

#output {
    margin-top: 16px;
}

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <script src="./script.js" async></script>
    <link href="./stylesheet.css" rel="stylesheet">
    <title>Caret Position</title>
</head>
<body>
    <p class="editor" contenteditable="true"><em>Write<br></em><br>some <br>awesome <b><em>text </em></b>here...</p>
    <p id="output">Select some text above</p>
</body>
</html>