JSFiddle - React, Tailwind, and code Playground

HTML

<body>
        <div class="header">
            <div class="logo_bg_left">
                <p class="logo_text_left">
                    Текст должен быть слева
                </p><!--logo_text_left-->
            </div><!--logo_bg_left-->
            <div class="logo_bg_right">
                <p class="logo_text_right">
                    Текст должен быть справа
                </p><!--logo_text_right-->
            </div><!--logo_bg_right-->
        </div><!--header-->
    </body>

CSS

* {
    margin: 0;
    padding: 0;
}

body {
    background: #E0E0E0;
}

.header {
    height: 100px;
    width: 950px;
    background: #2A3646;
    margin: 15px auto;
    border-radius: 3px;
}

.logo_bg_left {
    float: left;
    width: 250px;
    height: 50px;
    background: #083C82;
    margin-top: 20px;
    margin-left: 4px;
    border-radius: 15px;
}

.logo_text_left {
    color: #D4CC86;
    font-size: 16px;
    font-family: Verdana, sans-serif;
    padding: 13px 18px;
}

.logo_bg_right {
    float: right;    
    width: 250px;
    height: 50px;
    background: #395E2D;
    margin-top: 20px;
    margin-right: 4px;
    border-radius: 15px;
}

.logo_text_right {
    color: #D4CC86;
    font-size: 16px;
    font-family: Verdana, sans-serif;
    padding: 13px 18px;
}