To use the following function to retrieve the user email from the SharePoint User Profile service, you would need to pass in the account name of the user.

GetUserEmail = (function () {
    "use strict";
    var _webUrl = "http://myurl.com";
    var load = function (selectedValue) {

        $.ajax({
            cache: false,
           url: _webUrl + "/_api/SP.UserProfiles.PeopleManager/GetPropertiesFor(accountName=@v)?@v='" + encodeURIComponent(selectedValue) + "'&$select=Email",

            type: 'GET',
            headers: {
                "Accept": "application/json;odata=verbose"
            },
            success: function (data) {
                alert(JSON.stringify(data));
                var email = data.d.Email;
                $("#EmailContainer").val(email);

            }, 
            error: function (response) {
                alert(response.status + "  " + response.statusText);
            }

        });

    };
    return {
        load: load
    };
}());