\documentclass[a4paper, 12pt]{article}

% a nice font
\usepackage{kpfonts}

% basic text stuff
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}

\usepackage{tikz} % main tikz package
\usepackage{pgfplots} % pgplots package

\pgfplotsset{
    compat = 1.17, % to have the same coordinate system between axis and draw
}

\usepackage{tikz-network} % provides graph / network utilities (Edge, Node, etc)


\usetikzlibrary{arrows.meta} % for nice arrows
\usetikzlibrary{calc} % to do some computations on the coordinates

% for a nicer colorscheme
%\input{colors.tex}

\begin{document}

    % tangent plane formula from some stack exchange post
    \begin{tikzpicture}[>=stealth',tangent plane/.style args={at #1 with vectors #2 and #3}{insert path={#1 --  ($#1+($#2-(0,0,0)$)$) --  ($#1+($#2-(0,0,0)$)+($#3-(0,0,0)$)$) -- ($#1+($#3-(0,0,0)$)$) -- cycle}}]
        \begin{axis}[%
            axis equal,
            hide axis,
            width=10cm,
            height=10cm,
            axis lines = center,
            xlabel = {},
            ylabel = {},
            zlabel = {},
            ticks=none,
            enlargelimits=0.3,
            colormap={whiteblue}{color=(blue) color=(white)},
            colormap={gb}{color=(green) color=(yellow)
                color=(brown)},
            view/h=45,
            scale uniformly strategy=units only,
        ]
        \addplot3[%
            opacity = 0.95,
            z buffer = sort,
            surf,
            samples = 23,
            variable = \u,
            variable y = \v,
            domain = 0:360,
            y domain = 0:180,
            colormap={slategraywhite}{rgb255=(97,130,181) rgb255=(218, 192, 166)},
        ]
        ({sin(u)*cos(v)}, {sin(u)*sin(v)}, {cos(u)});

        \draw[fill=white,fill opacity=0.4,
            tangent plane=at {({cos(65)-0.5*sin(65)},-0.5,{sin(65)})} with
            vectors {({sin(65)},0,{-cos(65)})} and {(0,1,0)}];

        \end{axis}

        % I used trial and errors to find nice coordinates for those next nodes
        \coordinate (x) at (4.3,5);

        \draw[fill] (x) circle (0.03) node[below] {$x$};

        \draw[->] (x) to node[left] {$e_1$} (4.02,5.35) ;
        \draw[->] (x) to (4.7,5.21) node[below] {$e_2$};

    \end{tikzpicture}
\end{document}