This is not really a dupe of #54122 or #53818.
This is related to the changed useragent string of IE 11 and ExtJS browser sniffing!
In the backend, there is a <meta http-equiv="X-UA-Compatible" content="IE=10" /> (typo3 6.2) or <meta http-equiv="X-UA-Compatible" content="IE=9" /> (typo3 4.7) , so the IE11 useragent string does not contain "like gecko" and is sniffed as "isGecko=false".
So the RTE works in the Typo3 backend.
But if you want to use the RTE in the frontend, and also want to stay in "IE=edge", the htmlarea fails to initialize because it is sniffed as "isGecko=true".
A short fix , in (typo3 4.7 and 6.2) file: typo3/sysext/rtehtmlarea/htmlarea/htmlarea.js:
--- src: Ext.isGecko ? 'javascript:void(0);' : (Ext.isWebKit ? 'javascript: \'' + HTMLArea.htmlEncode(this.config.documentType + this.config.blankDocument) + '\'' : HTMLArea.editorUrl + 'popups/blank.html')
+++ // IE11 sometime pretends to be "like gecko". That's ok for Ext DOM related work, but not for the security model
+++ src: (Ext.isGecko && typeof document.baseURI !== 'undefined') ? 'javascript:void(0);' : (Ext.isWebKit ? 'javascript: \'' + HTMLArea.htmlEncode(this.config.documentType + this.config.blankDocument) + '\'' : HTMLArea.editorUrl + 'popups/blank.html')
I think that in the long term, rtehtmlarea should avoid using ExtJS "useragent string based" browser sniffing.