IE11 “edge” mode is not supported for SharePoint 2013 and 2010

First of All, “Edge Browser” and “IE 11 in Edge mode” different things. Edge Browser is a sperate browser than IE 11.

OOB SharePoint pages use special tagging to explicitly avoid this mode – however who want to enable it or just wrote custom master pages where they did not disable it (Edge is the preferred document mode in IE11) may face the problems.

For SharePoint 2010:
Plan browser support (SharePoint Foundation 2010)
https://technet.microsoft.com/en-us/library/cc288142%28v=office.14%29.aspx#supportmatrix

For SharePoint 2013:
Plan browser support in SharePoint 2013
https://technet.microsoft.com/en-us/library/cc263526.aspx#browserdetail

it is not supported to use SP2010 or SP2013 with Internet Explorer 11 in Edge mode. Resolution is Add sites to the Compatibility View list to make some features work.

Edge Browser still is not supported for SharePoint 2010 but after lastest CU we have started to support Edge Browser in SharePoint 2013 but still IE 11 edge mode is not supported even for SharePoint 2013.